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

Présenté par : Jean-Pierre Serre

Karpenko, Nikita A.1
1 UPMC Univ. Paris 06, Institut de Mathématiques de Jussieu, 4, place Jussieu, 75252 Paris cedex 05, France
Comptes Rendus. Mathématique, Tome 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
Karpenko, Nikita A. 1

1 UPMC Univ. Paris 06, Institut de Mathématiques de Jussieu, 4, place Jussieu, 75252 Paris cedex 05, France 
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Karpenko, Nikita A. Isotropy of symplectic involutions. Comptes Rendus. Mathématique, Tome 348 (2010) no. 21-22, pp. 1151-1153. doi : 10.1016/j.crma.2010.10.005. http://www.numdam.org/articles/10.1016/j.crma.2010.10.005/

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[3] Fesenko, I.B.; Vostokov, S.V. 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] Karpenko, N.A. Hyperbolicity of orthogonal involutions, Doc. Math. Extra Volume: Andrei A. Suslin's Sixtieth Birthday (2010), pp. 371-389 (electronic)

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

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

[7] Knus, M.-A.; Merkurjev, A.; Rost, M.; Tignol, J.-P. 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] Tignol, J.-P. 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)

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