Comptes Rendus
no. 21-22
Algebra/Algebraic Geometry
Isotropy of symplectic involutions
[Isotropie d'involutions symplectiques]

Présenté par : Jean-Pierre Serre

Nikita A. Karpenko1
1 UPMC Univ. Paris 06, Institut de Mathématiques de Jussieu, 4, place Jussieu, 75252 Paris cedex 05, France
Comptes Rendus. Mathématique, Volume 348 (2010) no. 21-22, pp. 1151-1153.

Nous démontrons l'analogue symplectique du théorème d'isotropie des involutions orthogonales. Nous utilisons (une modification de) la méthode due à J.-P. Tignol initialement utilisée pour démontrer l'analogue symplectique du théorème d'hyperbolicité des involutions orthogonales.

We prove the symplectic analogue of the isotropy theorem for orthogonal involutions. We apply (a modification of) a method due to J.-P. Tignol originally applied to prove the symplectic analogue of the hyperbolicity theorem for orthogonal involutions.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.10.005
Nikita A. Karpenko 1

1 UPMC Univ. Paris 06, Institut de Mathématiques de Jussieu, 4, place Jussieu, 75252 Paris cedex 05, France 
@article{CRMATH_2010__348_21-22_1151_0,
     author = {Nikita A. Karpenko},
     title = {Isotropy of symplectic involutions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1151--1153},
     publisher = {Elsevier},
     volume = {348},
     number = {21-22},
     year = {2010},
     doi = {10.1016/j.crma.2010.10.005},
     language = {en},
}
TY  - JOUR
AU  - Nikita A. Karpenko
TI  - Isotropy of symplectic involutions
JO  - Comptes Rendus. Mathématique
PY  - 2010
SP  - 1151
EP  - 1153
VL  - 348
IS  - 21-22
PB  - Elsevier
DO  - 10.1016/j.crma.2010.10.005
LA  - en
ID  - CRMATH_2010__348_21-22_1151_0
ER  - 
%0 Journal Article
%A Nikita A. Karpenko
%T Isotropy of symplectic involutions
%J Comptes Rendus. Mathématique
%D 2010
%P 1151-1153
%V 348
%N 21-22
%I Elsevier
%R 10.1016/j.crma.2010.10.005
%G en
%F CRMATH_2010__348_21-22_1151_0
Nikita A. Karpenko. Isotropy of symplectic involutions. Comptes Rendus. Mathématique, Volume 348 (2010) no. 21-22, pp. 1151-1153. doi : 10.1016/j.crma.2010.10.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.10.005/

[1] I.S. Cohen On the structure and ideal theory of complete local rings, Trans. Amer. Math. Soc., Volume 59 (1946), pp. 54-106

[2] R. Elman; N. Karpenko; A. Merkurjev The Algebraic and Geometric Theory of Quadratic Forms, American Mathematical Society Colloquium Publications, vol. 56, American Mathematical Society, Providence, RI, 2008

[3] I.B. Fesenko; S.V. Vostokov Local Fields and Their Extensions, Translations of Mathematical Monographs, vol. 121, American Mathematical Society, Providence, RI, 2002 (With a foreword by I.R. Shafarevich)

[4] N.A. Karpenko Hyperbolicity of orthogonal involutions, Doc. Math. Extra Volume: Andrei A. Suslin's Sixtieth Birthday (2010), pp. 371-389 (electronic)

[5] N.A. Karpenko Isotropy of orthogonal involutions, 31 Jan. 2010 (11 p) | arXiv

[6] N. Karpenko; A. Merkurjev Essential dimension of quadrics, Invent. Math., Volume 153 (2003) no. 2, pp. 361-372

[7] M.-A. Knus; A. Merkurjev; M. Rost; J.-P. Tignol The Book of Involutions, American Mathematical Society Colloquium Publications, vol. 44, American Mathematical Society, Providence, RI, 1998 (with a preface in French by J. Tits)

[8] J.-P. Tignol Hyperbolicity of symplectic and unitary involutions. Appendix to a paper of N. Karpenko, Doc. Math. Extra Volume: Andrei A. Suslin's Sixtieth Birthday (2010), pp. 389-392 (electronic)

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

Incompressibility of orthogonal grassmannians

Nikita A. Karpenko

C. R. Math (2011)

Classification of upper motives of algebraic groups of inner type An

Charles De Clercq

C. R. Math (2011)

Motivic decompositions of projective homogeneous varieties and change of coefficients

Charles De Clercq

C. R. Math (2010)