Catalogue et commandes en ligne (paiement sécurisé, VISA ou MASTERCARD uniquement)

Revues disponibles par abonnement

Annales scientifiques de l'ENS

Astérisque

Bulletin de la SMF

Mémoires de la SMF

Revue d'Histoire des Mathématiques

Gazette des Mathématiciens

Séries de livres

Astérisque

Cours Spécialisés

Documents Mathématiques

Mémoires de la SMF

Panoramas et Synthèses

Séminaires et Congrès

Série Chaire Jean Morlet

SMF/AMS Texts and Monographs

La Série T

Fascicules « Journée Annuelle »

Autres livres

Donald E. Knuth - traductions françaises

Rééditions du Séminaire Nicolas Bourbaki

Rééditions des Œuvres de Jean Leray

Revue de l'Institut Elie Cartan

Editions électroniques

Annales scientifiques de l'ENS

Bulletin de la SMF

Revue d'Histoire des Mathématiques

Séminaires et Congrès

Plus d'information / Abonnement

Publications grand public

L'explosion des mathématiques (smf.emath.fr)

Mathématiques L'explosion continue (smf.emath.fr)

Zoom sur les métiers des maths (smf.emath.fr)

Zoom sur les métiers des mathématiques et de l'informatique (smf.emath.fr)

Où en sont les mathématiques ?

La Série T

Pour les auteurs

Soumission des manuscrits

Formats et documentation

Plus d'info

Liste de diffusion électronique (smf.emath.fr)

Information pour les libraires et diffuseurs (smf.emath.fr)

Publications de la SMF
fr en
Votre numéro IP : 54.158.50.26
Accès aux édit. élec. : SémCong

Cours spécialisés

Présentation de la publication

Parutions

Dernières parutions

Comité de rédaction / Secrétariat

Volume :

Faire une recherche


Catalogue & commande

Cours spécialisés - Parutions - 15 (2008)

Parutions

Formes quadratiques sur un corps
Bruno Kahn
Cours spécialisés 15 (2008), x+303 pages
Acheter l'ouvrage

Résumé :
Ce livre expose la théorie des formes quadratiques sur un corps, en mettant l'accent sur la technique de Pfister-Arason-Knebusch d'extension des scalaires aux corps de fonctions de quadriques.

Mots-clefs : Formes quadratiques, corps de fonctions de quadriques, déploiement générique

Abstract:
Quadratic forms over a field
This book presents the theory of quadratic forms over a field, focusing on the Pfister-Arason-Knebusch technique of extensions to function fields of quadrics.

Keywords: Quadratic forms, function fields of quadrics, generic splitting

Class. math. : 11E04, 11E81


ISBN : 978-2-85629-261-7
ISSN : 1284-6090

Bibliographie:

1
Ahmad, Hamza
On quadratic forms over inseparable quadratic extensions
Arch. Math. (Basel) 63 (1994) 23–29
Math Reviews MR1277906
Zentralblatt 812.11027
2
Ahmad, Hamza
The algebraic closure in function fields of quadratic forms in characteristic 2
Bull. Austral. Math. Soc. 55 (1997) 293–297
Math Reviews MR1438847
Zentralblatt 880.11035
3
Ahmad, Hamza
Witt kernels of bi-quadratic extensions in characteristic 2
Bull. Austral. Math. Soc. 69 (2004) 433–440
Math Reviews MR2066661
Zentralblatt 1053.11032
4
Amitsur, S. A. and Rowen, Louis H. and Tignol, Jean-Pierre
Division algebras of degree 4 and 8 with involution
Israel J. Math. 33 (1979) 133–148
Math Reviews MR571249
5
André, Yves
Motifs de dimension finie (d'après S.-I. Kimura, P. O'Sullivan)
Astérisque Astérisque 299 (2005) 115–145 Séminaire Bourbaki. Vol. 2003/2004, Exp. no 929
Math Reviews MR2167204
Zentralblatt 1080.14010
6
André, Yves and Kahn, Bruno
Nilpotence, radicaux et structures monoïdales (avec un appendice de P. O'Sullivan)
Rend. Sem. Mat. Univ. Padova 108 (2002) 107–291
Math Reviews MR1956434
7
André, Yves and Kahn, Bruno
Erratum: ``Nilpotence, radicaux et structures monoïdales''
Rend. Sem. Mat. Univ. Padova 113 (2005) 125–128
Math Reviews MR2168984
8
Arason, Jón Kristinn
Cohomologische invarianten quadratischer Formen
J. Algebra 36 (1975) 448–491
Math Reviews MR0389761
Zentralblatt 314.12104
9
Arason, Jón Kristinn
Wittring und Galoiscohomologie bei Charakteristik 2
J. reine angew. Math. 307/308 (1979) 247–256
Math Reviews MR534222
Zentralblatt 396.12019
10
Arason, Jón Kristinn
A proof of Merkurjev's theorem
in Quadratic and Hermitian forms (Hamilton, Ont., 1983)
CMS Conf. Proc. 4 (1984) 121–130
Math Reviews MR776449
Zentralblatt 556.10009
11
Arason, Jón Kristinn
Excellence of F()/F for 2-fold Pfister forms
appendice II de [51]
12
Arason, Jón Kristinn and Knebusch, Manfred
Über die Grade quadratischer Formen
Math. Ann. 234 (1978) 167–192
Math Reviews MR0506027
13
Arason, Jón Kristinn and Pfister, Albrecht
Beweis des Krullschen Durchschnittsatzes für den Wittring
Invent. Math. 12 (1971) 173–176
Math Reviews MR0294251
14
Aravire, Roberto and Baeza, Ricardo
A note on generic splitting of quadratic forms
Comm. Algebra 27 (1999) 3473–3477
Math Reviews MR1695558
15
Aravire, Roberto and Baeza, Ricardo
The behavior of quadratic and differential forms under function field extensions in characteristic two
J. Algebra 259 (2003) 361–414
Math Reviews MR1955526
16
Aravire, Roberto and Baeza, Ricardo
Linkage of fields in characteristic 2
Comm. Algebra 31 (2003) 463–473
Math Reviews MR1969233
17
Aravire, Roberto and Baeza, Ricardo
Quadratic and differentials forms over function fields of Pfister quadrics in characteristic 2
(2005)
18
Aravire, Roberto and Jacob, Bill
The Milnor sequence for WqF(x) in characteristic 2 when F is perfect
in Algebraic and arithmetic theory of quadratic forms
Contemp. Math. 344 (2004) 1–17
Math Reviews MR2058664
19
Arf, Cahit
Untersuchungen über quadratische Formen in Körpern der Charakteristik 2. I
J. reine angew. Math. 183 (1941) 148–167
Math Reviews MR0008069
20
Artin, Emil and Nesbitt, Cecil J. and Thrall, Robert M.
Rings with Minimum Condition
University of Michigan Press, 1944
Math Reviews MR0010543
21
Baeza, Ricardo
Ein Teilformensatz für quadratische Formen in Charakteristik 2
Math. Z. 135 (1973/74) 175–184
Math Reviews MR0337765
22
Baeza, Ricardo
Quadratic forms over semilocal rings
Springer, 1978
Math Reviews MR0491773
Zentralblatt 382.10014
23
Baeza, Ricardo
The norm theorem for quadratic forms over a field of characteristic 2
Comm. Algebra 18 (1990) 1337–1348
Math Reviews MR1059733
Zentralblatt 711.11019
24
Baeza, Ricardo
Some algebraic aspects of quadratic forms over fields of characteristic two
in Proceedings of the Conference on Quadratic Forms and Related Topics (Baton Rouge, LA, 2001)
Doc. Math. extra vol., Quadratic forms LSU (2001) 49–63
Math Reviews MR1869388
Zentralblatt 1075.11022
25
Balmer, Paul
Witt cohomology, Mayer-Vietoris, homotopy invariance and the Gersten conjecture
K-Theory 23 (2001) 15–30
Math Reviews MR1852452
Zentralblatt 987.19002
26
Balmer, Paul
Witt groups
in Handbook of K-theory
2 (2007) 539–576
27
Balmer, Paul and Walter, Charles
A Gersten-Witt spectral sequence for regular schemes
Ann. Sci. École Norm. Sup. 35 (2002) 127–152
Math Reviews MR1886007
28
Bass, H. and Tate, J.
The Milnor ring of a global field
in Algebraic K-theory, II: ``Classical'' algebraic K-theory and connections with arithmetic (Proc. Conf., Seattle, Wash., Battelle Memorial Inst., 1972)
Lecture Notes in Math. 342 (1973) 349–446
Math Reviews MR0442061
29
Blanchard, André
Les corps non commutatifs
Presses Universitaires de France, 1972 Collection Sup: Le Mathématicien, No. 9
Math Reviews MR0354765
Zentralblatt 249.16001
30
Borel, Armand
Linear algebraic groups
Springer, 1991
Math Reviews MR1102012
Zentralblatt 726.20030
31
Bourbaki, N.
Éléments de Mathématiques, Algèbre
Hermann, 1958
32
Bourbaki, N.
Éléments de Mathématiques, Topologie générale
Hermann, 1960
33
Bourbaki, N.
Éléments de Mathématiques, Algèbre commutative
Hermann, 1961
34
Brosnan, Patrick
A short proof of Rost nilpotence via refined correspondences
Doc. Math. 8 (2003) 69–78
Math Reviews MR2029161
Zentralblatt 1044.11017
35
Brosnan, Patrick
Steenrod operations in Chow theory
Trans. Amer. Math. Soc. 355 (2003) 1869–1903
Math Reviews MR1953530
Zentralblatt 1045.55005
36
Cartan, Henri and Eilenberg, Samuel
Homological algebra
Princeton Univ. Press, 1956
Math Reviews MR0077480
37
Cartier, Pierre
Questions de rationalité des diviseurs en géométrie algébrique
Bull. Soc. Math. France 86 (1958) 177–251
Math Reviews MR0106223
Zentralblatt 091.33501
38
Cassels, J. W. S.
On the representation of rational functions as sums of squares
Acta Arith. 9 (1964) 79–82
Math Reviews MR0162791
Zentralblatt 131.25001
39
Cassels, J. W. S.
Rational quadratic forms
Academic Press Inc., 1978
Math Reviews MR522835
Zentralblatt 395.10029
40
Chernousov, Vladimir and Gille, Stefan and Merkurjev, Alexander S.
Motivic decomposition of isotropic projective homogeneous varieties
Duke Math. J. 126 (2005) 137–159
Math Reviews MR2110630
41
Chevalley, C.
Sur les décompositions cellulaires des espaces G/B
in Algebraic groups and their generalizations: classical methods (University Park, PA, 1991)
Proc. Sympos. Pure Math. 56 (1994) 1–23 avec un avant-propos d'Armand Borel
Math Reviews MR1278698
Zentralblatt 824.14042
42
Colliot-Thélène, Jean-Louis and Ojanguren, Manuel
Variétés unirationnelles non rationnelles: au-delà de l'exemple d'Artin-Mumford
Invent. Math. 97 (1989) 141–158
43
Colliot-Thélène, Jean-Louis and Skorobogatov, Alexei N.
Groupe de Chow des zéro-cycles sur les fibrés en quadriques
K-Theory 7 (1993) 477–500
Math Reviews MR1255062
44
Colliot-Thélène, Jean-Louis and Sujatha, R.
Unramified Witt groups of real anisotropic quadrics
in K-theory and algebraic geometry: connections with quadratic forms and division algebras (Santa Barbara, CA, 1992)
Proc. Sympos. Pure Math. 58.2 (1995) 127–147
Math Reviews MR1327294
45
Demazure, M.
Motifs de variétés algébriques
Lecture Notes in Math. 180 (1971) 19–38 Séminaire Bourbaki, exp. 365
46
Dickson, L. E.
On quadratic forms in a general field
Bull. Amer. Math. Soc. 14 (1907) 108–115 Math. papers IV, Chelsea, 1975, p. 512–519
Math Reviews MR1558550
47
Edidin, Dan and Graham, William
Equivariant intersection theory
Invent. Math. 131 (1998) 595–634
Math Reviews MR1614555
48
Elman, Richard and Karpenko, Nikita A. and Merkurjev, Alexander S.
The algebraic and geometric theory of quadratic forms
Amer. Math. Soc., 2008
49
Elman, Richard and Lam, T. Y.
Pfister forms and K-theory of fields
J. Algebra 23 (1972) 181–213
Math Reviews MR0302739
50
Elman, Richard and Lam, T. Y. and Tignol, Jean-Pierre and Wadsworth, Adrian R.
Witt rings and Brauer groups under multiquadratic extensions. I
Amer. J. Math. 105 (1983) 1119–1170
Math Reviews MR714772
51
Elman, Richard and Lam, T. Y. and Wadsworth, Adrian R.
Amenable fields and Pfister extensions
in Conference on Quadratic Forms—1976 (Proc. Conf., Queen's Univ., Kingston, Ont., 1976)
Pure Appl. Math. 46 (1977) 445–492
Math Reviews MR0560497
52
Elman, Richard and Lam, T. Y. and Wadsworth, Adrian R.
Pfister ideals in Witt rings
Math. Ann. 245 (1979) 219–245
Math Reviews MR553342
53
Faivre, F.
Liaison des formes de Pfister et corps de fonctions de quadriques en caractéristique 2
Thèse, Université de Franche-Comté (2006)
54
Fitzgerald, Robert W.
Function fields of quadratic forms
Math. Z. 178 (1981) 63–76
55
Fitzgerald, Robert W.
Witt kernels of function field extensions
Pacific J. Math. 109 (1983) 89–106
Math Reviews MR716291
Zentralblatt 486.10016
56
Fitzgerald, Robert W.
Quadratic forms of height two
Trans. Amer. Math. Soc. 283 (1984) 339–351
Math Reviews MR735427
Zentralblatt 512.10011
57
Friedlander, Eric M.
Motivic complexes of Suslin and Voevodsky
Astérisque Astérisque 245 (1997) 355–378 Séminaire Bourbaki, Vol.1996/97, Exp.no 833
Math Reviews MR1627118
Zentralblatt 908.19005
58
Fulton, William
Intersection theory
Springer, 1984
Math Reviews MR732620
Zentralblatt 541.14005
59
Garibaldi, S.
Cohomological invariants: exceptional groups and spin groups
Amer. Math. Soc., à paraître
60
Geel, J. (van)
Applications of the Riemann-Roch theorem for curves to quadratic forms and division algebras
UCL, Recherches de math. 7 (1991) 1–32
61
Gille, Philippe and Szamuely, Tamás
Central simple algebras and Galois cohomology
Cambridge Univ. Press, 2006
Math Reviews MR2266528
62
Greenberg, Marvin J.
Lectures on forms in many variables
W. A. Benjamin, Inc., New York-Amsterdam, 1969
Math Reviews MR0241358
63
Grothendieck, Alexander
Sur quelques points d'algèbre homologique
Tôhoku Math. J. 9 (1957) 119–221
Math Reviews MR0102537
64
Harrison, D. K.
A Grothendieck ring of higher degree forms
J. Algebra 35 (1975) 123–138
Math Reviews MR0379370
Zentralblatt 309.15016
65
Hartshorne, Robin
Algebraic geometry
Springer, 1977 Graduate Texts in Mathematics, No. 52
Math Reviews MR0463157
Zentralblatt 367.14001
66
Hoffmann, Detlev W.
On 6-dimensional quadratic forms isotropic over the function field of a quadric
Comm. Algebra 22 (1994) 1999–2014
Math Reviews MR1268540
Zentralblatt 804.11031
67
Hoffmann, Detlev W.
Isotropy of 5-dimensional quadratic forms over the function field of a quadric
in K-theory and algebraic geometry: connections with quadratic forms and division algebras (Santa Barbara, CA, 1992)
Proc. Sympos. Pure Math. 58.2 (1995) 217–225
Math Reviews MR1327299
Zentralblatt 824.11023
68
Hoffmann, Detlev W.
Isotropy of quadratic forms over the function field of a quadric
Math. Z. 220 (1995) 461–476
Math Reviews MR1362256
Zentralblatt 840.11017
69
Hoffmann, Detlev W.
On quadratic forms of height two and a theorem of Wadsworth
Trans. Amer. Math. Soc. 348 (1996) 3267–3281
Math Reviews MR1355298
Zentralblatt 867.11024
70
Hoffmann, Detlev W.
Twisted Pfister forms
Doc. Math. 1 (1996) No. 03, 67–102
Math Reviews MR1386048
Zentralblatt 853.11027
71
Hoffmann, Detlev W.
Sur les dimensions des formes quadratiques de hauteur 2
C. R. Acad. Sci. Paris Sér. I Math. 324 (1997) 11–14
Math Reviews MR1435579
Zentralblatt 879.11016
72
Hoffmann, Detlev W.
On the dimensions of anisotropic forms in I^4
Invent. Math. 131 (1998) 185–198
73
Hoffmann, Detlev W.
Splitting patterns and invariants of quadratic forms
Math. Nachr. 190 (1998) 149–168
Math Reviews MR1611608
Zentralblatt 916.11022
74
Hoffmann, Detlev W.
Diagonal forms of degree p in characteristic p
in Algebraic and arithmetic theory of quadratic forms
Contemp. Math. 344 (2004) 135–183
Math Reviews MR2058673
Zentralblatt 1074.11023
75
Hoffmann, Detlev W.
Witt kernels of bilinear forms for algebraic extensions in characteristic 2
Proc. Amer. Math. Soc. 134 (2006) 645–652
Math Reviews MR2180880
Zentralblatt pre02237898
76
Hoffmann, Detlev W. and Laghribi, Ahmed
Quadratic forms and Pfister neighbors in characteristic 2
Trans. Amer. Math. Soc. 356 (2004) 4019–4053
Math Reviews MR2058517
77
Hoffmann, Detlev W. and Laghribi, Ahmed
Isotropy of quadratic forms over the function field of a quadric in characteristic 2
J. Algebra 295 (2006) 362–386
Math Reviews MR2194958
78
Hoffmann, Detlev W. and Tignol, Jean-Pierre
On 14-dimensional quadratic forms in I3, 8-dimensional forms in I2, and the common value property
Doc. Math. 3 (1998) 189–214
Math Reviews MR1647511
79
Huber, Annette and Kahn, Bruno
The slice filtration and mixed Tate motives
Compos. Math. 142 (2006) 907–936
Math Reviews MR2249535
80
Hurrelbrink, Jürgen and Karpenko, Nikita A. and Rehmann, Ulf
The minimal height of quadratic forms of given dimension
Arch. Math. (Basel) 87 (2006) 522–529
Math Reviews MR2283683
81
Hurrelbrink, Jürgen and Rehmann, Ulf
Splitting patterns of excellent quadratic forms
J. reine angew. Math. 444 (1993) 183–192
Math Reviews MR1241799
82
Hurrelbrink, Jürgen and Rehmann, Ulf
Splitting patterns of quadratic forms
Math. Nachr. 176 (1995) 111–127
Math Reviews MR1361129
83
Izhboldin, Oleg T.
On the nonexcellence of field extensions F()/F
Doc. Math. 1 (1996) No. 06, 127–136
Math Reviews MR1386051
Zentralblatt 857.11017
84
Izhboldin, Oleg T.
Motivic equivalence of quadratic forms
Doc. Math. 3 (1998) 341–351
Math Reviews MR1668530
Zentralblatt 957.11019
85
Izhboldin, Oleg T.
On the isotropy of low-dimensional forms over function fields of a quadric
Algebra i Analiz 12 (2000) 106–127 traduction anglaise: St. Petersburg Math. J., 12 (2001), p. 791–805
Math Reviews MR1812943
86
Izhboldin, Oleg T.
Fields of u-invariant 9
Ann. of Math. 154 (2001) 529–587
87
Izhboldin, Oleg T. and Karpenko, Nikita A.
Isotropy of six-dimensional quadratic forms over function fields of quadrics
J. Algebra 209 (1998) 65–93
Math Reviews MR1652181
88
Izhboldin, Oleg T. and Karpenko, Nikita A.
Isotropy of 8-dimensional quadratic forms over function fields of quadrics
Comm. Algebra 27 (1999) 1823–1841
Math Reviews MR1679707
89
Izhboldin, Oleg T. and Karpenko, Nikita A.
Isotropy of virtual Albert forms over function fields of quadrics
Math. Nachr. 206 (1999) 111–122
Math Reviews MR1711554
90
Izhboldin, Oleg T. and Karpenko, Nikita A.
Some new examples in the theory of quadratic forms
Math. Z. 234 (2000) 647–695
Math Reviews MR1778404
91
Izhboldin, Oleg T. and Vishik, Alexander
Quadratic forms with absolutely maximal splitting
in Quadratic forms and their applications (Dublin, 1999)
Contemp. Math. 272 (2000) 103–125
Math Reviews MR1803363
92
Jacob, Bill and Rost, Markus
Degree four cohomological invariants for quadratic forms
Invent. Math. 96 (1989) 551–570
Math Reviews MR996554
93
Jacobson, N.
Some applications of Jordan norms to involutorial simple associative algebras
Adv. in Math. 48 (1983) 149–165
Math Reviews MR700981
94
Jannsen, Uwe
Motives, numerical equivalence, and semi-simplicity
Invent. Math. 107 (1992) 447–452
Math Reviews MR1150598
Zentralblatt 762.14003
95
Kahn, Bruno
Quelques remarques sur le u-invariant
Sém. Théor. Nombres Bordeaux 2 (1990) 155–161
Math Reviews MR1061764
Zentralblatt 712.12002
96
Kahn, Bruno
The total Stiefel-Whitney class of a regular representation
J. Algebra 144 (1991) 214–247
Math Reviews MR1136904
Zentralblatt 777.20019
97
Kahn, Bruno
A descent problem for quadratic forms
Duke Math. J. 80 (1995) 139–155
Math Reviews MR1360614
Zentralblatt 858.11024
98
Kahn, Bruno
Lower H-cohomology of higher-dimensional quadrics
Arch. Math. (Basel) 65 (1995) 244–250
Math Reviews MR1344022
99
Kahn, Bruno
Formes quadratiques de hauteur et de degré 2
Indag. Math. (N.S.) 7 (1996) 47–66
Math Reviews MR1621344
Zentralblatt 866.11030
100
Kahn, Bruno
La conjecture de Milnor (d'après V. Voevodsky)
Astérisque Astérisque 245 (1997) 379–418 Séminaire Bourbaki, Vol.1996/97, Exp.no 834
Math Reviews MR1627119
Zentralblatt 916.19001
101
Kahn, Bruno
Motivic cohomology of smooth geometrically cellular varieties
in Algebraic K-theory (Seattle, WA, 1997)
Proc. Sympos. Pure Math. 67 (1999) 149–174
Math Reviews MR1743239
Zentralblatt 954.19004
102
Kahn, Bruno
On ``horizontal'' invariants attached to quadratic forms
in Algebra and number theory
(2005) 21–33
Math Reviews MR2193343
Zentralblatt 1099.11020
103
Kahn, Bruno and Laghribi, Ahmed
A second descent problem for quadratic forms
K-Theory 29 (2003) 253–284
Math Reviews MR2029080
104
Kahn, Bruno and Rost, Markus and Sujatha, R.
Unramified cohomology of quadrics. I
Amer. J. Math. 120 (1998) 841–891
Math Reviews MR1637963
105
Kahn, Bruno and Sujatha, R.
Motivic cohomology and unramified cohomology of quadrics
J. Eur. Math. Soc. 2 (2000) 145–177
Math Reviews MR1763303
106
Kahn, Bruno and Sujatha, R.
Unramified cohomology of quadrics. II
Duke Math. J. 106 (2001) 449–484
Math Reviews MR1813233
107
Karpenko, Nikita A.
Invariants algébro-géométriques de formes quadratiques
Algebra i Analiz 2 (1990) 141–162 traduction anglaise: Leningrad Math. J 2 (1991), p. 119–138
Math Reviews MR1049908
Zentralblatt 791.11019
108
Karpenko, Nikita A.
Torsion in CH2 of Severi-Brauer varieties and indecomposability of generic algebras
Manuscripta Math. 88 (1995) 109–117
Math Reviews MR1348794
109
Karpenko, Nikita A.
Cohomologie d'espaces cellulaires relatifs et de variétés de drapeaux isotropes
Algebra i Analiz 12 (2000) 3–69 traduction anglaise: St. Petersburg Math. J 12 (2001), p. 1–50
110
Karpenko, Nikita A.
On anisotropy of orthogonal involutions
J. Ramanujan Math. Soc. 15 (2000) 1–22
Math Reviews MR1751923
Zentralblatt 962.16015
111
Karpenko, Nikita A.
Characterization of minimal Pfister neighbors via Rost projectors
J. Pure Appl. Algebra 160 (2001) 195–227
Math Reviews MR1836000
Zentralblatt 998.11016
112
Karpenko, Nikita A.
On the first Witt index of quadratic forms
Invent. Math. 153 (2003) 455–462
Math Reviews MR1992018
Zentralblatt 1032.11016
113
Karpenko, Nikita A.
Holes in In
Ann. Sci. École Norm. Sup. 37 (2004) 973–1002
Math Reviews MR2119244
114
Karpenko, Nikita A.
A relation between higher Witt indices
in Proceedings of the St. Petersburg Mathematical Society. Vol. XI
Amer. Math. Soc. Transl. Ser. 2 218 (2006) 77–86
Math Reviews MR2279306
115
Karpenko, Nikita A. and Merkurjev, Alexander S.
Rost projectors and Steenrod operations
Doc. Math. 7 (2002) 481–493
Math Reviews MR2015051
116
Karpenko, Nikita A. and Merkurjev, Alexander S.
Essential dimension of quadrics
Invent. Math. 153 (2003) 361–372
Math Reviews MR1992016
117
Kato, Kazuya
A generalization of local class field theory by using K-groups. I
J. Fac. Sci. Univ. Tokyo Sect. IA Math. 26 (1979) 303–376
Math Reviews MR550688
Zentralblatt 428.12013
118
Kato, Kazuya
Symmetric bilinear forms, quadratic forms and Milnor K-theory in characteristic two
Invent. Math. 66 (1982) 493–510
Math Reviews MR662605
Zentralblatt 497.18017
119
Knebusch, Manfred
Grothendieck- und Wittringe von nichtausgearteten symmetrischen Bilinearformen
S.-B. Heidelberger Akad. Wiss. Math.-Natur. Kl. (1969/1970) 93–157
Math Reviews MR0271118
120
Knebusch, Manfred
Specialization of quadratic and symmetric bilinear forms, and a norm theorem
Acta Arith. 24 (1973) 279–299
Math Reviews MR0349582
Zentralblatt 287.15010
121
Knebusch, Manfred
Generic splitting of quadratic forms. I
Proc. London Math. Soc. 33 (1976) 65–93
Math Reviews MR0412101
Zentralblatt 351.15016
122
Knebusch, Manfred
Generic splitting of quadratic forms. II
Proc. London Math. Soc. 34 (1977) 1–31
Math Reviews MR0427345
Zentralblatt 359.15013
123
Knebusch, Manfred
Symmetric bilinear forms over algebraic varieties
in Conference on Quadratic Forms—1976 (Proc. Conf., Queen's Univ., Kingston, Ont., 1976)
Queen's Univ., 1977
Math Reviews MR0498378
Zentralblatt 408.15019
124
Knebusch, Manfred
Spezialisierung von quadratischen und symmetrisch bilinearen Formen
livre en préparation, http://www.math.uni-bielefeld.de/LAG/man/289.html
125
Knebusch, Manfred and Rehmann, Ulf
Generic splitting towers and generic splitting preparation of quadratic forms
in Quadratic forms and their applications (Dublin, 1999)
Contemp. Math. 272 (2000) 173–199
Math Reviews MR1803367
126
Knebusch, Manfred and Scharlau, Winfried
Algebraic theory of quadratic forms
Birkhäuser, 1980 Generic methods and Pfister forms, Notes taken by Heisook Lee
Math Reviews MR583195
127
Knus, Max-Albert
Quadratic forms, Clifford algebras and spinors
Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Ciência da Computação, Campinas, 1988
Math Reviews MR1099376
Zentralblatt 742.11018
128
Knus, Max-Albert
Quadratic and Hermitian forms over rings
Springer, 1991
Math Reviews MR1096299
Zentralblatt 756.11008
129
Knus, Max-Albert and Merkurjev, Alexander S. and Rost, Markus and Tignol, Jean-Pierre
The book of involutions
AMS, 1998
130
Laghribi, Ahmed
Isotropie de certaines formes quadratiques de dimensions 7 et 8 sur le corps des fonctions d'une quadrique
Duke Math. J. 85 (1996) 397–410
Math Reviews MR1417621
Zentralblatt 865.11030
131
Laghribi, Ahmed
Formes quadratiques en 8 variables dont l'algèbre de Clifford est d'indice 8
K-Theory 12 (1997) 371–383
Math Reviews MR1485435
Zentralblatt 893.11016
132
Laghribi, Ahmed
Formes quadratiques de dimension 6
Math. Nachr. 204 (1999) 125–135
Math Reviews MR1705142
Zentralblatt 927.11023
133
Laghribi, Ahmed
Sur le problème de descente des formes quadratiques
Arch. Math. (Basel) 73 (1999) 18–24
Math Reviews MR1696572
Zentralblatt 927.11022
134
Laghribi, Ahmed
Sur les formes quadratiques de hauteur 3 et de degré au plus 2
Doc. Math. 4 (1999) 203–217
Math Reviews MR1701294
Zentralblatt 922.11030
135
Laghribi, Ahmed
Certaines formes quadratiques de dimension au plus 6 et corps des fonctions en caractéristique 2
Israel J. Math. 129 (2002) 317–361
Math Reviews MR1910948
Zentralblatt 1049.11040
136
Laghribi, Ahmed
On the generic splitting of quadratic forms in characteristic 2
Math. Z. 240 (2002) 711–730
Math Reviews MR1922726
Zentralblatt 1007.11017
137
Laghribi, Ahmed
On splitting of totally singular quadratic forms
Rend. Circ. Mat. Palermo 53 (2004) 325–336
138
Laghribi, Ahmed
Quasi-hyperbolicity of totally singular quadratic forms
in Algebraic and arithmetic theory of quadratic forms
Contemp. Math. 344 (2004) 237–248
Math Reviews MR2060200
Zentralblatt pre02154490
139
Laghribi, Ahmed
Witt kernels of function field extensions in characteristic 2
J. Pure Appl. Algebra 199 (2005) 167–182
Math Reviews MR2134299
Zentralblatt pre02175024
140
Laghribi, Ahmed
The norm theorem for totally singular quadratic forms
Rocky Mountain J. Math. 36 (2006) 575–592
Math Reviews MR2234821
Zentralblatt pre05249768
141
Laghribi, Ahmed
Witt kernels of quadratic forms for purely inseparable multiquadratic extensions in characteristic 2
Proc. Amer. Math. Soc. 134 (2006) 2481–2486
Math Reviews MR2213724
Zentralblatt pre05023942
142
Laghribi, Ahmed
Sur le déploiement des formes bilinéaires en caractéristique 2
Pacific J. Math. 232 (2007) 207–232
Math Reviews MR2358037
143
Laghribi, Ahmed and Mammone, Pasquale
Isotropie d'une forme quadratique sur le corps des fonctions d'une quadrique en caractéristique 2
Bull. Belg. Math. Soc. 9 (2002) 167–176
Math Reviews MR2017073
144
Laghribi, Ahmed and Mammone, Pasquale
On the norm theorem for semisingular quadratic forms
Indag. Math. (N.S.) 17 (2006) 599–610
Math Reviews MR2320116
145
Lam, T. Y.
Ten lectures on quadratic forms over fields
in Conference on Quadratic Forms—1976 (Proc. Conf., Queen's Univ., Kingston, Ont., 1976)
Queen's Univ., 1977
Math Reviews MR0498380
Zentralblatt 396.10008
146
Lam, T. Y.
Fields of u-invariant 6 after A. Merkurjev [A. S. Merkur'ev]
in Ring theory 1989 (Ramat Gan and Jerusalem, 1988/1989)
Israel Math. Conf. Proc. 1 (1989) 12–30
Math Reviews MR1029293
147
Lam, T. Y.
Introduction to quadratic forms over fields
Amer. Math. Soc., 2005
Math Reviews MR2104929
Zentralblatt 1068.11023
148
Leep, D. B.
Function field results
(1989)
149
Lewis, David W. and Van Geel, Jan
Quadratic forms isotropic over the function field of a conic
Indag. Math. (N.S.) 5 (1994) 325–339
Math Reviews MR1298779
150
Loeser, François
Cobordisme des variétés algébriques (d'après M. Levine et F. Morel)
Astérisque Astérisque 290 (2003) 167–192 Séminaire Bourbaki. Vol. 2001/2002, Exp. no 901
Math Reviews MR2074055
151
Lorentz, F.
Quadratische Formen über Körpern
Springer Verlag, 1970
152
Lorenz, F. and Leicht, J.
Die Primideale des Wittschen Ringes
Invent. Math. 10 (1970) 82–88
Math Reviews MR0266949
153
Mac Lane, Saunders
Categories for the working mathematician
Springer, 1998
Math Reviews MR1712872
Zentralblatt 906.18001
154
Mammone, Pasquale and Moresi, Remo
Formes quadratiques, algèbres à division et extensions multiquadratiques inséparables
Bull. Belg. Math. Soc. 2 (1995) 311–319
Math Reviews MR1338463
155
Mammone, Pasquale and Shapiro, Daniel B.
The Albert quadratic form for an algebra of degree four
Proc. Amer. Math. Soc. 105 (1989) 525–530
Math Reviews MR931742
156
Mammone, Pasquale and Tignol, Jean-Pierre and Wadsworth, Adrian R.
Fields of characteristic 2 with prescribed u-invariants
Math. Ann. 290 (1991) 109–128
Math Reviews MR1107665
157
Manin, Ju. I.
Correspondances, motifs et transformations monoïdales
Mat. Sb. (N.S.) 77 (119) (1968) 475–507 traduction anglaise: Math. USSR Sbornik 6 (1968), p. 439–470
Math Reviews MR0258836
158
Merkurjev, Alexander S.
Simple algebras over function fields of quadrics
(1989)
159
Merkurjev, Alexander S.
Simple algebras and quadratic forms
Izv. Akad. Nauk SSSR 55 (1991) 218–224 traduction anglaise: Math. USSR Izv. 36 (1991), p. 349–368
160
Merkurjev, Alexander S.
On the norm residue homomorphism for fields
in Mathematics in St. Petersburg
Amer. Math. Soc. Transl. Ser. 2 2 (1996) 49–71
Zentralblatt 876.12005
161
Merkurjev, Alexander S.
On the norm residue homomorphism of degree two
in Proceedings of the St. Petersburg Mathematical Society. Vol. XII
Amer. Math. Soc. Transl. Ser. 2 219 (2006) 103–124
Math Reviews MR2276853
162
Merkurjev, Alexander S. and Suslin, A. A.
The norm residue homomorphism of degree 3
Izv. Akad. Math. SSSR 54 (1990) 339–356 traduction anglaise: Math. USSR Izv. 36 (1991), p. 349–368
163
Milnor, John
Algebraic K-theory and quadratic forms
Invent. Math. 9 (1969/1970) 318–344
Math Reviews MR0260844
164
Milnor, John
Symmetric inner products in characteristic 2
in Prospects in mathematics (Proc. Sympos., Princeton Univ., Princeton, N.J., 1970)
Annals of Math. Studies 70 (1971) 59–75
Math Reviews MR0347866
Zentralblatt 265.10013
165
Milnor, John and Husemoller, Dale
Symmetric bilinear forms
Springer, 1973 Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 73
Math Reviews MR0506372
166
Morel, Fabien
Suite spectrale d'Adams et invariants cohomologiques des formes quadratiques
C. R. Acad. Sci. Paris Sér. I Math. 328 (1999) 963–968
Math Reviews MR1696188
Zentralblatt 937.19002
167
Morel, Fabien
An introduction to A1-homotopy theory
in Contemporary developments in algebraic K-theory
ICTP Lect. Notes, XV 15 (2004) 357–441
Math Reviews MR2175638
168
Morel, Fabien
Milnor's conjecture on quadratic forms and mod 2 motivic complexes
Rend. Sem. Mat. Univ. Padova 114 (2005) 63–101
Math Reviews MR2207862
Zentralblatt pre05058746
169
Morel, Fabien and Voevodsky, Vladimir
A1-homotopy theory of schemes
Publ. Math. Inst. Hautes Études Sci. 90 (1999) 45–143
Math Reviews MR1813224
170
Nekovář, Jan
On the parity of ranks of Selmer groups. III
Doc. Math. 12 (2007) 243–274
Math Reviews MR2350290
Zentralblatt pre05165891
171
Ojanguren, Manuel
The Witt group and the problem of Lüroth
Dottorato di Ricerca in Matematica (1990)
Math Reviews MR1077830
172
O'Meara, O. T.
Introduction to quadratic forms
Springer, 1963
Zentralblatt 107.03301
173
Orlov, D. and Vishik, Alexander and Voevodsky, Vladimir
An exact sequence for KM/2 with applications to quadratic forms
Ann. of Math. 165 (2007) 1–13
Math Reviews MR2276765
174
Parimala, R.
Witt groups of conics, elliptic, and hyperelliptic curves
J. Number Theory 28 (1988) 69–93
Math Reviews MR925609
Zentralblatt 696.14016
175
Parimala, R. and Suresh, V.
On the length of a quadratic form
in Algebra and number theory
(2005) 147–157
Math Reviews MR2193350
176
Peyre, Emmanuel
Products of Severi-Brauer varieties and Galois cohomology
in K-theory and algebraic geometry: connections with quadratic forms and division algebras (Santa Barbara, CA, 1992)
Proc. Sympos. Pure Math. 58.2 (1995) 369–401
Math Reviews MR1327310
Zentralblatt 837.14006
177
Pfister, Albrecht
Multiplikative quadratische Formen
Arch. Math. (Basel) 16 (1965) 363–370
Math Reviews MR0184937
178
Pfister, Albrecht
Zur Darstellung von -1 als Summe von Quadraten in einem Körper
J. London Math. Soc. 40 (1965) 159–165
Math Reviews MR0175893
179
Pfister, Albrecht
Quadratische Formen in beliebigen Körpern
Invent. Math. 1 (1966) 116–132
Math Reviews MR0200270
180
Pfister, Albrecht
Zur Darstellung definiter Funktionen als Summe von Quadraten
Invent. Math. 4 (1967) 229–237
Math Reviews MR0222043
Zentralblatt 222.10022
181
Pfister, Albrecht
Quadratic lattices in function fields of genus 0
Proc. London Math. Soc. 66 (1993) 257–278
Math Reviews MR1199066
Zentralblatt 808.11025
182
Pfister, Albrecht
Quadratic forms with applications to algebraic geometry and topology
Cambridge Univ. Press, 1995
Math Reviews MR1366652
Zentralblatt 847.11014
183
Pierce, Richard S.
Associative algebras
Springer, 1982
Math Reviews MR674652
Zentralblatt 497.16001
184
Racine, M. L.
A simple proof of a theorem of Albert
Proc. Amer. Math. Soc. 43 (1974) 487–488
Math Reviews MR0330218
Zentralblatt 285.16013
185
Rost, Markus
On quadratic forms isotropic over the function field of a conic
Math. Ann. 288 (1990) 511–513
Math Reviews MR1079875
Zentralblatt 698.12009
186
Rost, Markus
Hilbert theorem 90 for K_3^M for a quadratic extension
prépublication, Univ. Regensburg, 1986
187
Rost, Markus
On 14-dimensional forms, their spinors and the difference of two octonion algebras
prépublication, Univ. Regensburg, 1994
188
Rowen, Louis H.
Division algebras of exponent 2 and characteristic 2
J. Algebra 90 (1984) 71–83
189
Rowen, Louis H.
Ring theory I
Academic Press Inc., 1988
Math Reviews MR1095047
Zentralblatt 743.16001
190
Schafer, Richard D.
An introduction to nonassociative algebras
Academic Press, 1966
Math Reviews MR0210757
191
Scharlau, Winfried
Quadratic forms
Queen's University, 1969
Math Reviews MR0269679
192
Scharlau, Winfried
Quadratic and Hermitian forms
Springer, 1985
Math Reviews MR770063
Zentralblatt 584.10010
193
Schneider, J. E.
Orthogonal groups of nonsingular forms of higher degree
J. Algebra 27 (1973) 112–116
Math Reviews MR0325795
Zentralblatt 287.20038
194
Scholl, A. J.
Classical motives
in Motives (Seattle, WA, 1991)
Proc. Sympos. Pure Math. 55 (1994) 163–187
Math Reviews MR1265529
Zentralblatt 814.14001
195
Serre, Jean-Pierre
Groupes algébriques et corps de classes
Publications de l'institut de mathématique de l'université de Nancago, VII. Hermann, Paris, 1959
Math Reviews MR0103191
Zentralblatt 097.35604
196
Serre, Jean-Pierre
Corps locaux
Publications de l'institut de mathématique de l'université de Nancago, VIII. Hermann, Paris, 1968
Math Reviews MR0354618
197
Serre, Jean-Pierre
Cours d'arithmétique
Presses universitaires de France, 1978
198
Serre, Jean-Pierre
Cohomologie galoisienne
Springer, 1994
Math Reviews MR1324577
Zentralblatt 812.12002
199
Shapiro, Daniel B.
Similarities, quadratic forms, and Clifford algebras
Thèse, Université de Berkeley (1974)
200
Sivatski, A. S.
Nonexcellence of multiquadratic field extensions
J. Algebra 275 (2004) 859–866
Math Reviews MR2052642
Zentralblatt 1133.11027
201
Springer, Tonny Albert
Sur les formes quadratiques d'indice zéro
C. R. Acad. Sci. Paris 234 (1952) 1517–1519
Math Reviews MR0047021
Zentralblatt 046.24303
202
Springer, Tonny Albert
Quadratic forms over fields with a discrete valuation. I. Equivalence classes of definite forms
Nederl. Akad. Wetensch. Proc. Ser. A. 58 = Indag. Math. 17 (1955) 352–362
Math Reviews MR0070664
203
Suslin, A. A.
The quaternion homomorphism for the field of functions on a conic
Dokl. Akad. Nauk SSSR 265 (1982) 292–296 traduction anglaise: Soviet Math. Dokl. 26 (1982), p. 72–77
Math Reviews MR665314
204
Suslin, A. A.
Torsion in K2 of fields
K-theory 1 (1987) 5–29
205
Swan, Richard G.
Zero cycles on quadric hypersurfaces
Proc. Amer. Math. Soc. 107 (1989) 43–46
Math Reviews MR979219
Zentralblatt 718.14007
206
Szyjewski, M.
Le cinquième invariant des formes quadratiques
Algebra Anal. 2 (1990) 213–234 traduction anglaise: Leningrad Math. J. 2 (1991), p. 179–198
207
Tignol, Jean-Pierre
Sur les classes de similitude de corps à involution de degré 8
C. R. Acad. Sci. Paris Sér. A-B 286 (1978) A875–A876
Math Reviews MR0498496
Zentralblatt 374.16006
208
Tignol, Jean-Pierre
Algèbres indécomposables d'exposant premier
Adv. in Math. 65 (1987) 205–228
Math Reviews MR904723
Zentralblatt 642.16015
209
Tignol, Jean-Pierre
Réduction de l'indice d'une algèbre simple centrale sur le corps des fonctions d'une quadrique
Bull. Soc. Math. Belg. Sér. A 42 (1990) 735–745
Math Reviews MR1316221
Zentralblatt 736.12002
210
Totaro, B.
Birational geometry of quadrics in characteristic 2
J. Alg. Geom. 17 (2008) 577–597
211
Vishik, Alexander
Integral motives of quadrics
13 (1998) 1–82
212
Vishik, Alexander
On dimensions of anisotropic forms in I^n
11 (2000) 1–41
213
Vishik, Alexander
Motives of quadrics with applications to the theory of quadratic forms
in Geometric methods in the algebraic theory of quadratic forms
Lecture Notes in Math. 1835 (2004) 25–101
Math Reviews MR2066515
Zentralblatt 1047.11033
214
Vishik, Alexander
Fields of u-invariant 2^r+1
(2007)
215
Voevodsky, Vladimir
Cancellation theorem
(2000) prépublication
216
Voevodsky, Vladimir
Triangulated categories of motives over a field
in Cycles, transfers, and motivic homology theories
Ann. of Math. Stud. 143 (2000) 188–238
Math Reviews MR1764202
Zentralblatt 1019.14009
217
Voevodsky, Vladimir
Motivic cohomology with <b>Z</b>/2-coefficients
Publ. Math. Inst. Hautes Études Sci. 98 (2003) 59–104
Math Reviews MR2031199
218
Voevodsky, Vladimir
Reduced power operations in motivic cohomology
Publ. Math. Inst. Hautes Études Sci. 98 (2003) 1–57
Math Reviews MR2031198
Zentralblatt 1057.14027
219
Wadsworth, Adrian R.
Noetherian pairs and function fields of quadratic forms
Thèse, Université de Chicago (1972)
220
Wadsworth, Adrian R.
Similarity of quadratic forms and isomorphism of their function fields
Trans. Amer. Math. Soc. 208 (1975) 352–358
Math Reviews MR0376527
Zentralblatt 336.15013
221
Wadsworth, Adrian R.
Merkurjev's elementary proof of Merkurjev's theorem
in Applications of algebraic K-theory to algebraic geometry and number theory, Part I, II (Boulder, Colo., 1983)
Contemp. Math. 55 (Vol. II) (1986) 741–776
Math Reviews MR862663
Zentralblatt 604.16022
222
Wall, C. T. C.
Graded Brauer groups
J. reine angew. Math. 213 (1963/1964) 187–199
Math Reviews MR0167498
223
Witt, Ernst
Über ein Gegenbeispiel zum Normensatz
Math. Z. 39 (1935) 462–467
Math Reviews MR1545510
224
Witt, Ernst
Theorie der quadratischen Formen in beliebigen Körpern
J. reine angew. Math. 176 (1937) 31–44
225
Witt, Ernst
Œuvres
Springer, 1998