Comptes Rendus
Algebra/Algebraic Geometry
Isotropy of symplectic involutions
Comptes Rendus. Mathématique, Volume 348 (2010) no. 21-22, pp. 1151-1153.

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.

Received:
Accepted:
Published online:
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
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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/

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[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)

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