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 : 54.198.221.13
Accès aux édit. élec. : SémCong

Annales scientifiques de l'ENS

Présentation de la publication

Parutions

Dernières parutions

Comité de rédaction / Secrétariat

Série 4 :
Série 3 :
Série 2 :
Série 1 :

Faire une recherche


Catalogue & commande

Annales scientifiques de l'ENS - Parutions - série 4, 50 (2017)

Parutions < série 4, 50

ANNALES SCIENTIFIQUES DE L’ÉCOLE NORMALE SUPÉRIEURE, série 4 50, fascicule 2 (2017)

Julia Gordon, David Roe
The canonical measure on a reductive p-adic group is motivic
Annales scientifiques de l'ENS 50, fascicule 2 (2017), 345-355

Télécharger cet article : Fichier PDF

Résumé :
La mesure canonique sur un groupe réductif p-adique est motivique
Soit G un groupe algébrique réductif connexe sur un corps local non-archimédien. Dans ce papier, nous démontrons que ses sous-groupes parahoriques sont définissables dans le langage de Denef-Pas, qui est le langage utilisé dans la théorie d'intégration motivique de Cluckers et Loeser. Notre résultat principal établit que la composante connexe du modèle de Néron d'un tore modérément ramifié est définissable. Ce résultat implique que la mesure canonique sur G (qui donne le volume 1 à un sous-groupe parahorique spécifique, défini par Gross [4]), est une mesure motivique. Ce résultat permet une simplification de quelques preuves dans [9] et [1, Appendix B]. Finalement, nous montrons que le degré formel des représentations supercuspidales dans une famille paramétrique est une fonction motivique des paramètres.

Mots-clefs : Modèle de Néron, langage de Denef-Pas, tore algébrique, mesure canonique.

Abstract:
Let G be a connected reductive group over a non-Archimedean local field. We prove that its parahoric subgroups are definable in the Denef-Pas language, which is a first-order language of logic used in the theory of motivic integration developed by Cluckers and Loeser. The main technical result is the definability of the connected component of the Néron model of a tamely ramified algebraic torus. As a corollary, we prove that the canonical Haar measure on G, which assigns volume 1 to the particular canonical maximal parahoric defined by Gross in [4], is motivic. This result resolves a technical difficulty that arose in [9] and [1, Appendix B] and permits a simplification of some of the proofs in those articles. It also allows us to show that formal degree of a compactly induced representation is a motivic function of the parameters defining the representation.

Keywords: Néron models, Denef-Pas language, algebraic tori, canonical measure.

Class. math. : 22E50; 20G25, 14E18, 03C60.


ISSN : 0012-9593
Publié avec le concours de : Centre National de la Recherche Scientifique

Bibliographie:

1
Shin, Sug Woo and Templier, Nicolas
Sato-Tate theorem for families and low-lying zeroes of automorphic L-functions, with appendices by R. Kottwitz and J. Gordon, R. Cluckers and I. Halupczok
Invent. math. 203 (2016) 1–177
2
Kottwitz, Robert
Isocrystals with additional structure. II
Compos. math. 109 (1997) 255–339
3
4
Gross, Benedict H.
On the motive of a reductive group
Invent. math. 130 (1997) 287–313
5
Cluckers, Raf and Loeser, François
Constructible motivic functions and motivic integration
Invent. math. 173 (2008) 23–121
6
Gordon, Julia and Hales, Thomas
Endoscopic transfer of orbital integrals in large residual characteristic
Amer. J. Math. 138 (2016) 109–148
7
Cluckers, Raf and Hales, Thomas and Loeser, François
Transfer principle for the Fundamental Lemma
in On the stabilization of the Trace Formula
(2011)
8
Cluckers, Raf and Gordon, Julia and Halupczok, Immanuel
Motivic functions, integrability, and applications to harmonic analysis on p-adic groups
Electron. Res. Announc. 21 (2014) 137–152
9
Cluckers, Raf and Gordon, Julia and Halupczok, Immanuel
Local integrability results in harmonic analysis on reductive groups in large positive characteristic
Ann. sci. Éc. Norm. Sup. 47 (2014) 1163–1195
10
Cluckers, Raf and Gordon, Julia and Halupczok, Immanuel
Integrability of oscillatory functions on local fields: transfer principles
Duke Math Journal 163 (2014) 1549–1600
11
Bitan, Rony A.
The discriminant of an algebraic torus
J. Number Theory 131 (2011) 1657–1671
12
Brahm, Bernhard
Néron-Modelle algebraischer Tori
in Néron-Modelle algebraischer Tori
Universität Münster, 2004
13
Adams, Jeffrey and Vogan, David
Contragredient representations and characterizing the local Langlands correspondence
(2012) ArXiv 1201.0496 [math.RT]
14
Benoist, Yves and Quint, Jean-François
Introduction to random walks on homogeneous spaces
Japanese Journal of Mathematics 7 (2012) 135–166
15
Buzzard, Kevin
Eigenvarieties
in L-functions and Galois representations
London Math Soc. Lecture Note Ser., no. 320 (2007) 59–120
16
Wan, Daqing and Xiao, Liang and Zhang, Jun
Slopes of eigencurves over boundary disks
(2014) arXiv 1407.0279
17
18
Fontaine, Jean-Marc
Périodes p-adiques
in Périodes p-adiques
Société Mathématique de France, 1994
19
Caruso, Xavier and Lubicz, David
Semi-simplified modulo p of semi-stable representations: an algorithmic approach
(2013) arXiv 1309.4194 [math.NT]
20
Kedlaya, Kiran S.
p-adic differential equations
in p-adic differential equations
Cambridge UP, 2010
21
Hales, Thomas
Can p-adic integrals be computed?
in Contributions to automorphic forms, geometry, and number theory
(2004) 313–329
22
Cluckers, Raf and Cunningham, Clifton and Gordon, Julia and Spice, Loren
On the computability of some positive-depth characters near the identity
Representation Theory 15 (2011) 531–567
23
Caruso, Xavier and Vaccon, Tristan and Roe, David
Tracking p-adic precision
LMS Journal of Computation and Mathematics 17 (Special issue A) (2014) 274-294
24
Bernstein, Joseph and Luntz, Valery
Equivariant sheaves and functors
Springer, 1994
25
26
Weibel, Charles A.
An introduction to homological algebra
Cambridge U.P., 1994
27
Bernstein, Joseph
Stacks in Representation Theory: What is a representation of an algebraic group?
28
Bitan, Rony A.
The discriminant of an algebraic torus
J. Number Theory 131 (2011) 1657–1671
29
Grothendieck, Alexandre
Éléments de géométrie algébrique IV. Étude locale des schémas et des morphismes de schémas. III
Publ. Math. IHÉS 28 (1966)
30
Rabin, Michael O.
Computable algebra, general theory and theory of computable fields
Transactions of the AMS 95 (1960) 341–360
31
Rockafellar, R. Tyrell
Variational Analysis
in Variational Analysis
Springer, 1997
32
Lauder, Alan
Deformation theory and the computation of zeta functions
Proc. London Math. Soc. 88 (2004) 565–602
Math Reviews MR2044050 (2005g:11166)
33
Ellenberg, Jordan and Jain, Sonal and Venkatesh, Akshay
Modelling -invariants by p-adic random matrices
Communications on Pure and Applied Mathematics 64 (2011) 1243–1262
34
Trefethen, Lloyd N. and David Bau III
Numerical Linear Algebra
in Numerical Linear Algebra
SIAM, 1997
35
Adams, Jeffrey and Vogan, David
L-groups, projective representations, and the Langlands classification
Amer. J. Math. 113 (1991) 45-138
36
Roe, David
Constructing local L-packets for tame unitary groups
(2013) arXiv:1311.7456
37
Morris, Lawrence
Some tamely ramified supercuspidal representations of symplectic groups
Proc. London Math. Soc. 63 (1991) 519–551
38
Berthomieu, Jérémy and van der Hoeven, Joris and Lecerf, Grégoire
Relaxed algorithms for p-adic numbers
J. Théorie des Nombres des Bordeaux 23 (2011) 541–577
39
van der Hoeven, Joris
New algorithms for relaxed multiplication
J. Symbolic Comput. 42 (2007) 792-802
40
van der Hoeven, Joris
Relax, but don't be too lazy
J. Symbolic Comput. 34 (2002) 479-542
41
Somos, Michael
Problem 1470
Crux Mathematicorum 15 (1989) 208
42
Diao, Hansheg and Liu, Ruochuan
The eigencurve is proper
(2014) arXiv:1401.4871
43
Davis, Christopher and Wan, Daqing and Xiao, Liang
Newton slopes for Artin-Schreier-Witt towers
(2013) arXiv 1310:5311
44
Loeffler, David
Spectral expansions of overconvergent modular functions
Int. Math. Res. Notices (2007)
45
Kilford, Lloyd and McMurdy, Ken
Slopes of the U_7 operator acting on a space of overconvergent modular forms
LMS Journal of Computation and Mathematics 15 (2012) 113–139
46
Kilford, Lloyd
On the slopes of the U_5 operator acting on overconvergent modular forms
J. Théorie des Nombres des Bordeaux 20 (2008) 165–182
47
Coleman, Robert
Classical and overconvergent modular forms
Inventiones Math. 124 (1996) 215–241
48
49
Schneider, Peter
p-Adic Lie groups
in p-adic Lie groups
Springer, 2011
50
Lercier, Reynald and Sirvent, Thomas
On Elkies subgroups of -torsion points in elliptic curves defined over a finite field
J. Théorie des Nombres des Bordeaux 20 (2008) 783–797
51
Kedlaya, Kiran S.
Counting points on hyperelliptic curves using Monsky–Washnitzer cohomology
J. Ramanujan Math. Soc. 16 (2001) 323–338
52
Gaudry, Pierrick and Houtmann, Thomas and Weng, Annegret and Ritzenthaler, Christophe and Kohel, David
The 2-adic CM method for genus 2 curves with application to cryptography
in Asiacrypt 2006
LNCS 4284 (2006) 114–129
53
Fomin, Sergey and Zelevinsky, Andrei
The Laurent phenomenon
Advances in Applied Math. 28 (2002) 119–144
54
Caruso, Xavier and Lubicz, David
Linear algebra over Zp[[u]] and related rings
(2014) to appear in LMS J. Comp. and Math.
55
Caruso, Xavier
Random matrices over a DVR and LU factorization
(2012) arXiv:1212.0308
56
Bostan, Alin and González-Vega, Laureano and Perdry, Hervé and Schost, Éric
From Newton sums to coefficients: complexity issues in characteristic p
in MEGA'05
(2005)
57
Karatsuba, Anatolii and Ofman, Yuri
Multiplication of many-digital numbers by automatic computers
Proceedings of the USSR Academy of Sciences 145 (1962) 293–294
58
Kreidl, Martin
On p-adic loop groups and Grassmannians
(2010) arXiv:1010.0349v1
59
Bertrapelle, Alessandra and Gonzáles-Avilés, Cristian D.
On the cohomology of tori over local fields with perfect residue field
(2013) arXiv:1311.4841v3
60
Sebag, Julien and Nicaise, Johannes
Motivic Serre invariants and Weil restriction
J. Algebra 319 (2008) 1585-1610
61
62
Weber, Andreas
On Coherence in Computer Algebra
63
Xin, Guoce
The Ring of Malcev-Neumann Series and the Residue Theorem
64
Pauli, Sebastian
Constructing Class Fields over Local Fields
65
Gerkmann, Ralf
A quick introduction to Sage
66
GNU MP
in GNU MP
67
Aaronson, Scott
Polynomial Hierarchy Collapses
in Polynomial Hierarchy Collapses
68
Manin, Yuri
Frobenius Manifolds, Quantum Cohomology and Moduli Spaces
in Frobenius Manifolds, Quantum Cohomology and Moduli Spaces
69
Jaffe, Arthur
Introduction to Quantum Field Theory
70
Yap, Chee-Keng
Linear Systems
71
Saip, Herbert and Lucchesi, Claudio
Matching Algorithms for Bipartite Graphs
72
Mahajan, Meena and Vinjay, V
Determinant: Combinatorics, Algorithms and Complexity
73
Cook, William and Rohe, Andre
Computing minimum weight perfect matchings
74
Cluckers, Raf and Cunningham, Clifton and Gordon, Julia and Spice, Loren
On the computability of some positive-depth characters near the identity
Representation Theory 15 (2011) 531-567
75
Trac 9977: Implement complex multiplication for points of CM elliptic curves
76
Nash-Williams, Crispin
Well-balanced orientations on finite graphs and unobtrusive odd-vertex-pairings
in Recent progress in combinatorics (Proc. Third Waterloo Conf. on Combinatorics)
(1969) 133-149
77
Trac 9293: Better expose GAP's character tables from Sage
78
Trac 7303: Nash-William theorem on orientation of graph
79
Trac 7368: Further work on isogenies and endomorphisms of elliptic curves
80
Buzzard, Kevin and Kilford, Lloyd
The 2-adic eigencurve at the boundary of weight space
Compos. math. 141 (2005) 605-619
81
Smithline, Lawren
Slopes of p-adic modular forms
Thèse, University of California at Berkeley (2000)
82
Serre, Jean-Pierre
Completely continuous endomorphisms of p-adic Banach spaces
Publ. Math. IHÉS 12 (1962) 69-85
83
84
Jacobs, Daniel
Slopes of compact Hecke operators
Thèse, Imperial College (2003)
85
Emerton, Matthew
2-adic modular forms of minimal slope
Thèse, Harvard University (1998)
86
Diamond, Fred and Shurman, Jerry
A first course in modular forms
in A first course in modular forms
Springer, 2005
87
Coleman, Robert and Mazur, Barry
The eigencurve
in Galois representations in algebraic geometry
London Math Soc. Lecture Note Ser., no. 254 (1998) 1-113
88
Coleman, Robert
Classical and overconvergent modular forms of higher level
J. Théor. Nombres Bordeaux 9 (1997) 395-403
89
Buzzard, Kevin
Harvard Course Math 254z
(2006)
90
Buzzard, Kevin and Calegari, Frank
Slopes of overconvergent 2-adic modular forms
Compos. math. 141 (2005) 591-604
91
Frenkel, Edward and Gaitsgory, Dennis
D-modules on the affine flag variety and representations of affine Kac-Moody algebras
Represent. Theory 13 (2009) 470-608
92
93
Sinclair, Brian and Pauli, Sebastian
Trac 12561: factoring p-adic polynomials
94
Gan, Wee Teck and Takeda, Shuichiro
The local Langlands conjecture for GSp(4)
Annals of Math 173 (2011) 1841-1882
95
Arthur, James
The endoscopic classification of representations: orthogonal and symplectic groups
in The endoscopic classification of representations: orthogonal and symplectic groups
American Math Society, 2013
96
LMFDB Collaboration, The
L-functions and modular forms database
97
Cremona, John
Elliptic curve data
(2012)
98
Hoshi, Akinari and Yamasaki, Aiichi
Rationality problem for algebraic tori
(2012) arXiv 1210.4525 [math.AG]
99
Dummit, Evan and Hablicsek, Marton and Harron, Robert and Jain, Lalit and Pollack, Robert and Ross, Daniel
Explicit computations of Hida families via overconvergent modular symbols
(2013) In preparation
100
Darmon, Henri
Efficient calculation of Stark-Heegner points via overconvergent modular symbols
Israel J. Math. 153 (2006) 319-354
101
Pollack, Rob and Stevens, Glenn
Overconvergent modular symbols and p-adic L-functions
Ann. sci. Éc. Norm. Sup. 44 (2011) 1-42
102
Rob Pollack, Rob Harron, David Roe, et al
Overconvergent Modular Symbols
103
Lusztig, George
Character sheaves III
Advances in Math. 57 (1985) 266-315
104
Deligne, Pierre and Lusztig, George
Representations of reductive groups over finite fields
Annals of Math 103 (1976) 103-161
105
Adrian, Moshe and Roe, David
Rectifiers and the local Langlands correspondence: the unramified case
(2013) ArXiv:1307.0469 [math.RT]
106
Cunningham, Clifton and Roe, David
From the function-sheaf dictionary to quasicharacters of p-adic tori
(2013) arXiv:1310.2988 [math.AG]
107
Kashiwara, Masaki and Schapira, Pierre
Categories and Sheaves
Springer, 2006
108
Waldspurger, Jean-Loup
Intégrales orbitales nilpotentes et endoscopie pour les groupes classiques non ramifiés
Astérisque 269 (2001)
109
Brown, Kenneth S.
Cohomology of groups
Springer, 1982
110
Grothendieck, Alexandre
Séminaire de Géométrie Algébrique du Bois Marie 1965–66 SGA5: Cohomologie -adique et Fonctions L
Springer, 1977
111
Warfield, Jr. R. B.
Decomposability of finitely presented modules
Proc. Amer. Math. Soc. 25 (1970) 167–172
112
Grothendieck, Alexandre
Éléments de géométrie algébrique IV. Étude locale des schémas et des morphismes de schémas. II
Publ. Math. IHÉS 24 (1965)
113
Lusztig, George
Character sheaves on disconnected groups I
Representation Theory 7 (2003) 374–403
114
The Stacks Project Authors
Stacks Project
in Stacks Project
(2013)
115
Greenberg, Marvin J.
Schemata over local rings I
Annals of Math 73 (1961) 624–648
116
Demazure, Michel and Gabriel, Pierre
Groupes algébriques
in Groupes algébriques. Tome 1: Géométrie algébrique, généralités, groupes commutatifs
Masson Cie, 1970
117
Serre, Jean-Pierre
Sur les corps locaux à corps résiduel algébriquement clos
Bull. Soc. Math. France 89 (1961) 105-154
118
Serre, Jean-Pierre
Groupes proalgébriques
Publ. Math. IHÉS 7 (1960)
119
Lusztig, George
Character sheaves I
Advances in Math. 56 (1985) 193-237
120
121
Suzuki, Takashi and Yoshida, Manabu
A refinement of the local class field theory of Serre and Hazewinkel
in Algebraic number theory and related topics
RIMS Kôkyûroku Bessatsu, B32 (2012) 163-191
122
123
Tate, John
Fourier analysis in number fields, and Hecke's zeta-functions
in Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965)
(1967) 305-347
124
Stasinski, Alexander
Reductive group schemes, the Greenberg functor, and associated algebraic groups
J. Pure Appl. Algebra 216 (2012) 1092-1101
125
Deligne, Pierre and Katz, Nicholas
Groupes de monodromie en géométrie algébrique II
in Groupes de monodromie en géométrie algébrique. II
Springer, 1973
126
Deligne, Pierre
Cohomologie étale
Springer, 1977
127
Laumon, Gérard
Transformation de Fourier, constantes d'équations fonctionnelles et conjecture de Weil
Publ. Math. IHÉS 65 (1987) 131-210
128
Kamgarpour, Masoud
Stacky abelianization of algebraic groups
Transform. Groups 14 (2009) 825-846
129
Grothendieck, Alexandre
Revêtements étales et groupe fondamental (SGA 1)
in Revêtements étales et groupe fondamental (SGA 1)
Institut des Hautes Études Scientifiques, 1963
130
Greenberg, Marvin J.
Schemata over local rings II
Annals of Math 78 (1963) 256-266
131
Deligne, Pierre
Les corps locaux de caractéristique p, limites de corps locaux de caractéristique 0
in Representations of reductive groups over a local field
Travaux en Cours (1984) 119-157
132
Deligne, Pierre
La conjecture de Weil II
Publ. Math. IHÉS 52 (1980) 137-252
133
Deligne, Pierre
Catégories tensorielles
Mosc. Math. J. 2 (2002) 227-248
134
Chai, Ching-Li and Yu, Jiu-Kang
Congruences of Néron models for tori and the Artin conductor
Annals of Math 154 (2001) 347-382
135
Chai, Ching-Li
Néron models for semiabelian varieties: congruence and change of base field
Asian J. Math. 4 (2000) 715-736
136
Brandal, Willy
Commutative rings whose finitely generated modules decompose
in Commutative rings whose finitely generated modules decompose
Springer, 1979
137
Belinson, Alexander A. and Bernstein, Joseph and Deligne, Pierre
Faisceaux pervers
Astérisque Astérisque 100 100 (1982) 5–171
138
Zaremsky, Matthew
Representatives of elliptic Weyl group elements in algebraic groups
(2011) Preprint, arXiv:1109.5487
139
Xarles, Xavier
The scheme of connected components of the Néron model of an algebraic torus
J. reine angew. Math. 437 (1993) 167-180
140
Tits, Jacques
Normalisateurs de tores
J. Algebra 4 (1966) 96-116
141
Atiyah, Michael and Wall, Charles
Cohomology of groups
in Algebraic number theory
(1967) 84-115
142
Serre, Jean-Pierre
Algebraic groups and class fields
in Algebraic Groups and Class Fields
Springer, 1988
143
Reeder, Mark
Supercuspidal L-packets of positive depth and twisted Coxeter elements
J. reine angew. Math. 620 (2008) 1-33
144
Murnaghan, Fiona
Parametrization of tame supercuspidal representations
in On certain L-functions: a volume in honor of Freydoon Shahidi on the occasion of his 60th birthday
Clay Math Proc. 13 (2011) 439-470
145
Kaletha, Tasho
Simple wild L-packets
J. Inst. Math. Jussieu 12 (2013) 43-75
146
Humphreys, James E.
Linear algebraic groups
in Linear Algebraic Groups
Springer, 1975
147
Howe, Roger
Tamely ramified supercuspidal representations of GL_n(F)
Pacific J. Math. 73 (1997) 437-460
148
Tam, Geo Kam-Fai
Transfer relations in essentially tame local Langlands correspondence
Thèse, University of Toronto (2012)
149
Bushnell, Colin and Kutzko, Phil
The admissible dual of GL(n) via compact open subgroups
in The admissible dual of GL(n) via compact open subgroups
Princeton U.P., 1993
150
Bushnell, Colin and Henniart, Guy
The essentially tame local Langlands correspondence, III: the general case
Proc. Lond. Math. Soc. 101 (2010) 497-553
151
Bushnell, Colin and Henniart, Guy
The essentially tame local Langlands correspondence, II: totally ramified representations
Compos. math. 141 (2005) 979-1011
152
Serre, Jean-Pierre
Local Class Field Theory
in Algebraic number theory
(1967) 129-162
153
Adrian, Moshe and Lansky, Joshua
A real groups construction of the tame local Langlands correspondence for PGSp(4,F)
(2012) Accepted at Israel J. Math., arXiv:1209.6045
154
Adrian, Moshe
A new realization of the Langlands correspondence for PGL(2,F)
Journal of Number Theory 133 (2013) 446-474
155
Adler, Jeffrey
Refined anisotropic K-types and supercuspidal representations
Pacific J. Math. (1998) 1-32
156
Bushnell, Colin and Henniart, Guy
To an effective local Langlands correspondence
(2011) ArXiv:1103.5316v1
157
Humphreys, James E.
Conjugacy Classes in Semisimple Algebraic Groups
in Conjugacy Classes in Semisimple Algebraic Groups
American Math Society, 1995
158
Lang, Serge
Algebraic Groups over Finite Fields
Amer. J. Math. 78 (1956) 555-563
159
Jacquet, Herve
Sur les représentations des groupes réductifs p-adiques
C. R. Acad. Sci. Paris 280 (1975) 1271-1272
160
Johnson, Arnold
Integral Representations of Hermitian Forms Over Local Fields
Journ. reine u. angewandte 229 (1968) 57-80
161
Haines, Thomas and Rapoport, Michael
On Parahoric Subgroups
Advances in Math. 219 (2008) 188-198
162
Steinberg, Robert
Endomorphisms of Linear Algebraic Groups
in Endomorphisms of Linear Algebraic Groups
American Math Society, 1968
163
Collingwood, David H. and McGovern, William M.
Nilpotent Orbits in Semisimple Lie Algebras: An Introduction
in Nilpotent Orbits in Semisimple Lie Algebras: An Introduction
Chapman and Hall/CRC, 1993
164
Henniart, Guy
La conjecture de Langlands locale pour (3)
Mémoires S.M.F. 11/12 (1984)
165
Scholze, Peter
The local Langlands correspondence for _n over p-adic fields
(2010) Preprint
166
Hiraga, Kaoru and Saito, Hiroshi
On L-packets for inner forms of _n
(2008) Preprint
167
Langlands, Robert
Representations of algebraic groups
(1968) Mimeographed notes, Yale University
168
Isaacs, I. Martin
Character Theory of Finite Groups
Academic Press, 1976
169
Demazure, Michel
Exposé XXIV: Automorphismes des groupes réductifs
in Schémas en groupes III: Structure des schemas en groupes reductifs
Lecture Notes in Math 153 (1970)
170
Iwasawa, Kenkichi
On galois groups of local fields
Transactions of the AMS 80 (1955) 448-469
171
Kottwitz, Robert
Stable trace formula: cuspidal tempered terms
Duke Math Journal 51 (1984) 611-650
172
Gan, Wee Teck and Gross, Benedict H. and Prasad, Dipendra
Symplectic local root numbers, central critical L-values and restriction problems in the representation theory of classical groups
(2009) to appear in Asterisque
173
Gross, Benedict H.
Heegner points and representation theory
in Heegner points and Rankin L-series
MSRI Publications 49 (2004) 37-65
174
Gerstein, Larry J.
Basic Quadratic Forms
in Basic Quadratic Forms
American Math Society, 2008
175
Jacobowitz, Ronald
Hermitian forms over local fields
American Journal of Mathematics 84 (1962) 441-465
176
Milne, James S.
Arithmetic Duality Theorems
in Arithmetic Duality Theoresm
BookSurge, LLC, 2006
177
178
179
Jahnel, Joerg
The Brauer-Severi variety associated with a central simple algebra
Linear Algebraic Groups and Related Structures 52 (2000) 1-60
180
Fulton, William and Harris, Joe
Representation Theory: A First Course
Springer, 1991
181
Néron, André
Modèles minimaux des variétés abéliennes sur les corps locaux et globaux
Publ. Much. IHÉS 21 (1964)
182
Schneider, Peter and Stuhler, Ulrich
Representation theory and sheaves on the Bruhat-Tits building
Inst. Hautes Études Sci. Publ. Math 85 (1997) 97-191
183
Garrett, Paul
Buildings and Classical Groups
in Buildings and Classical Groups
Chapman Hall, 1997
184
Yu, Jiu-Kang
Bruhat-Tits theory and buildings
in Ottowa Lectures on Admissible Representations of Reductive p-adic Groups
Fields Institute Monographs (2009) 53-76
185
Bruhat, Francois and Tits, Jacques
Groupes algébriques sur un corps local. Chapitre III. Compléments et applications à la cohomologie galoisienne
J. Fac. Sci. Univ. Tokyo Sect. IA Math. 34 (1987) 671-698
186
Bruhat, Francois and Tits, Jacques
Schémas en groupes et immeubles des groupes classiques sur un corps local. II
Bull. Soc. Math. France 115 (1987) 141-195
187
Bruhat, Francois and Tits, Jacques
Schémas en groupes et immeubles des groupes classiques sur un corps local
Bull. Soc. Math. France 112 (1984) 259-301
188
Tits, Jacques
Reductive groups over local fields
in Automorphic forms, representations and L-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis OR, 1977)
Proceedings of Symposia in Pure Mathematics XXXIII (1979) 29-69
189
Tate, John
Number theoretic background
in Automorphic forms, representations and L-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis OR, 1977)
Proceedings of Symposia in Pure Mathematics XXXIII (1979) 3-26
190
Cartan, Henri and Eilenberg, Samuel
Homological Algebra
Princeton U.P., 1956
191
Serre, Jean-Pierre
Galois Cohomology
in Galois Cohomology
Springer, 2001
192
193
Robert, Alain
A Course in p-adic Analysis
in A Course in p-adic Analysis
Springer, 2000
194
Algebraic Number Theory
London Math Society, 2010
195
Reeder, Mark
Elliptic centralizers in Weyl groups and their coinvariant representations
Representation Theory 15 (2011) 63-111
196
Waterhouse, William
Introduction to Affine Group Schemes
in Introduction to Affine Group Schemes
Springer, 1979
197
Borel, Armand
Automorphic L-functions
in Automorphic forms, representations and L-functions
Proceedings of Symposia in Pure Mathematics 33, part 2 (1979) 27-61
198
Vogan, David
The local Langlands conjecture
in Representation theory of groups and algebras
Representation Theory of Groups and Algebras Contemporary Mathematics 145 (1993)
199
Emerton, Matthew
Local-global compatibility in the p-adic Langlands programme for _2/
(2010)
200
Colmez, Pierre
Representations de _2() et (, )-modules
Asterisque 330 (2010) 281-509
201
Frenkel, Edward
Langlands correspondence for loop groups
in Langlands correspondence for loop groups
Cambridge UP, 2007
202
Jacquet, Herve and Langlands, Robert
Automorphic forms on (2)
in Automorphic forms on (2)
Springer, 1970
203
Humphreys, James E.
Reflection Groups and Coxeter Groups
in Reflection Groups and Coxeter Groups
Cambridge UP, 1990
204
Abramenko, Peter and Brown, Kenneth S.
Buildings
Springer, 2008
205
206
Joyner, David and Stein, WIlliam
Open Source Mathematical Software
Notices of the AMS 54 (2007) 1279
207
Loeffler, David
Explicit calculations of automorphic forms for definite unitary groups
LMS Journal of Computation and Mathematics 11 (2008) 326-342
208
Harvey, David
Kedlaya's algorithm in larger characteristic
Int. Math. Res. Notices (2007)
209
Bosma, Wieb and Cannon, John and Payoust, Catherine
The Magma algebra system. I. The user language.
J. Symbolic Comput. 24 (1997) 235-265
210
211
Prasad, Gopal and Yu, Jiu-Kang
On finite group actions on reductive groups and buildings
Inventiones Math. 147 (2002) 545-560
212
Jones, John and Roberts, David
A Database of Local Fields
J. Symbolic Comput. 41 (2006) 80-97
213
Guàrdia, Jordi and Montes, Jesús and Nart, Enric
Higher Newton polygons and integral bases
(2009) arXiv:0902.3428 [math.NT]
214
Guàrdia, Jordi and Montes, Jesús and Nart, Enric
Higher Newton polygons in the computation of discriminants and prime ideal decomposition in number fields
(2008) arXiv:0807.4065 [math.NT]
215
Guàrdia, Jordi and Montes, Jesús and Nart, Enric
Newton polygons of higher order in algebraic number theory
Transactions of the AMS 364 (2012) 361-416
216
Pauli, Sebastian
Factoring polynomials over local fields II
in Algorithmic Number Theory, 9th International Symposium
(2010)
217
Junkins, Caroline and Kolster, Manfred
An analogue of the Gauss class number problem in motivic cohomology
Annales mathématiques du Québec 37 (2013) 79-108
218
Balakrishnan, Jennifer S. and Bradshaw, Robert W. and Kedlaya, Kiran S.
Explicit Coleman integration for hyperelliptic curves
in Algorithmic Number Theory, 9th International Symposium
(2010)
219
Lansky, Joshua and Pollack, David
Hecke algebras and automorphic forms
Compos. math. 130 (2002) 21-48
220
Gross, Benedict H.
Algebraic modular forms
Israel J. Math. 113 (1999) 61-93
221
Knightly, Andrew and Li, Charles
Simple supercuspidal representations of (n)
(2013) Preprint
222
Geck, M. and Hiss, G. and Lübeck, F. and Malle, G. and Pfeiffer, G.
CHEVIE – A system for computing and processing generic character tables for finite groups of Lie type, Weyl groups and Hecke algebras
Appl. Algebra Engrg. Comm. Comput. 7 (1996) 175-210
223
Carter, Roger W.
Finite groups of Lie type: conjugacy classes and complex characters
in Finite Groups of Lie Type: conjugacy classes and complex characters
Wiley Sons, 1993
224
Bushnell, Colin and Henniart, Guy
The local Langlands conjecture for GL(2)
in The Local Langlands Conjecture for GL(2)
Springer, 2006
225
Loeffler, David and Weinstein, Jared
On the computation of local components of a newform
Mathematics of Computation 81 (2012) 1179-1200
226
GAP – Groups, Algorithms, and Programming
(1986-2013)
227
Batut, Christian and Belabas, Karim and Benardi, Dominique and Cohen, Henri and Olivier, Michel
User's guide to PARI-GP
(1985-2013)
228
Stein WilliamWilliam Stein et al
Sage Mathematics Software
(2005-2013)
229
Roe, David
The Local Langlands Correspondence for Tamely Ramified Groups
Thèse, Harvard University (2011)
230
Birch, Bryan and Swinnerton-Dyer, Peter
Notes on elliptic curves II
J. reine angew. Math. 218 (1965) 79-108
231
Henniart, Guy
Une preuve simple des conjectures de Langlands pour (n) sur un corps p-adique
Invent. math. 139 (2000) 439-455
232
Harris, Michael and Taylor, Richard
The geometry and cohomology of some simple Shimura varieties
in The geometry and cohomology of some simple Shimura varieties
Princeton U.P., 2001
233
An introduction to the Langlands program
in An Introduction to the Langlands Program
Birkhauser, 2004
234
Gelbart, Stephen
An elementary introduction to the Langlands program
Bull. Amer. Math. Soc. (N.S.) 10 (1984) 177-219
235
Wiles, Andrew J.
Modular elliptic curves and Fermat's last theorem
Annals of Math 141 (1995) 443-551
236
237
Khare, Chandrashekhar and Winterberger, Jean-Pierre
Serre's modularity conjecture
Inventiones Mathematicae 178 (2009) 485-586
238
Gross, Benedict H. and Reeder, Mark
Arithmetic invariants of discrete Langlands parameters
Duke Math Journal (2010) 431-508
239
Carter, Roger W.
Conjugacy classes in the Weyl group
Compos. math. 25 (1972) 1-59
240
DeBacker, Stephen and Reeder, Mark
Depth-zero supercuspidal L-packets and their stability
Annals of Math 169 (2009) 795-901
241
Bruhat, Francois and Tits, Jacques
Groupes réductifs sur un corps local, Chapitre II
Publ. Math. IHÉS 60 (1984) 197-376
242
Springer, T.A.
Linear Algebraic Groups
in Linear Algebraic Groups
Birkhäuser, 1998
243
Yu, Jiu-Kang
On the local Langlands correspondence for tori
in Ottawa Lectures on Admissible Representations of Reductive p-adic Groups
Fields Institute Monographs 26 (2009) 177–183
244
Reeder, Mark
Torsion automorphisms of simple Lie algebras
L'Enseignement mathematique 56 (2009) 3-47
245
Rapoport, Michael
A guide to the reduction modulo p of Shimura varieties
in A guide to the reduction modulo p of Shimura varieties
Astérisque 298 (2005) 271-318
246
Platonov, Vladimir and Rapinchuk, Andrei
Algebraic Groups and Number Theory
in Algebraic Groups and Number Theory
Academic Press, Inc., 1991
247
Bosch, Siegfried and Lütkebohmert, Werner and Raynaud, Michel
Néron models
in Neron Models
Springer, 1980
248
Yu, Jiu-Kang
Smooth models associated to concave functions in Bruhat-Tits theory
(2003) Preprint
249
Bruhat, Francois and Tits, Jacques
Groupes réductifs sur un corps local, Chapitre I
Publ. Math. IHÉS 41 (1972) 5-251
250
Moy, Allen and Prasad, Gopal
Jacquet functors and unrefined minimal K-types
Comment. Math. Helv. 71 (1996) 98-121
251
Serre, Jean-Pierre
Local Fields
Springer, 1979