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Bulletin de la SMF - Titles - 144 (2016) 763-773

Titles < 144

Incompressible Grassmannians of isotropic subspaces
Nikita A. Karpenko
Bulletin de la SMF 144, fascicule 4 (2016), 763-773

Télécharger cet article : Fichier PDF

Résumé :
Grassmanniennes incompressibles d'espaces isotropes
Nous étudions des grassmanniennes 2-incompressibles de sous-espaces isotropes d'une forme quadratique ainsi que d'une forme hermitienne au-dessus d'une extension quadratique du corps de base ou au-dessus d'une algèbre de quaternions.

Mots-clefs : Formes quadratiques, groupes algébriques, variétés projectives homogènes, grassmanniennes orthogonales, symplectiques et unitaires, groupes et motifs de Chow, dimension canonique et incompressibilité.

Abstract:
We study 2-incompressible Grassmannians of isotropic subspaces of a quadratic form, of a hermitian form over a quadratic extension of the base field, and of a hermitian form over a quaternion algebra.

Keywords: Quadratic forms, algebraic groups, projective homogeneous varieties, orthogonal, symplectic, and unitary Grassmannians, Chow groups and motives, canonical dimension and incompressibility.

Class. math. : 20G15, 14C25.


ISSN : 0037-9484
Publié avec le concours de : Centre National de la Recherche Scientifique

Bibliographie:

1
Elman, Richard and Karpenko, Nikita and Merkurjev, Alexander
The algebraic and geometric theory of quadratic forms
Amer. Math. Soc., Providence, RI, 2008
Math Reviews MR2427530
2
Fulton, William
Intersection theory
Springer, Berlin, 1998
Math Reviews MR1644323
3
4
5
Karpenko, Nikita A.
A bound for canonical dimension of the (semi)spinor groups
Duke Math. J. 133 (2006) 391–404
Math Reviews MR2225698
6
Karpenko, Nikita A.
Canonical dimension
in Proceedings of the International Congress of Mathematicians. Volume II
(2010) 146–161
Math Reviews MR2827789
7
Karpenko, Nikita A.
Sufficiently generic orthogonal Grassmannians
J. Algebra 372 (2012) 365–375
Math Reviews MR2990015
8
Karpenko, Nikita A.
Upper motives of algebraic groups and incompressibility of Severi-Brauer varieties
J. reine angew. Math. 677 (2013) 179–198
Math Reviews MR3039776
9
Karpenko, Nikita A.
Variations on a theme of rationality of cycles
Cent. Eur. J. Math. 11 (2013) 1056–1067
Math Reviews MR3036017
10
Karpenko, Nikita A.
Incompressibility of products of Weil transfers of generalized Severi-Brauer varieties
Math. Z. 279 (2015) 767–777
11
Karpenko, Nikita A. and Merkurjev, Alexander S.
Hermitian forms over quaternion algebras
Compos. Math. 150 (2014) 2073–2094
Math Reviews MR3292294
12
Karpenko, Nikita and Reichstein, Zinovy
A numerical invariant for linear representations of finite groups
Comment. Math. Helv. 90 (2015) 667–701
Math Reviews MR3420466
13
Karpenko, Nikita and Zhykhovich, Maksim
Isotropy of unitary involutions
Acta Math. 211 (2013) 227–253
Math Reviews MR3143890
14
Knus, Max-Albert and Merkurjev, Alexander and Rost, Markus and Tignol, Jean-Pierre
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Math Reviews MR1632779
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Merkurjev, Alexander S.
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Math Reviews MR3055773
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Math Reviews MR770063
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Math Reviews MR2066515
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Vishik, Alexander
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Math Reviews MR2148072
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Vishik, Alexander
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Math Reviews MR2305424
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Vishik, Alexander
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