Geodesic
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.

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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.

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.

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://geodesic.mathdoc.fr/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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