Incompressibility of orthogonal grassmannians

Nikita A. Karpenko

doi:10.1016/j.crma.2011.10.004

Algebra/Algebraic Geometry

Incompressibility of orthogonal grassmannians

Presented by: Claire Voisin

Nikita A. Karpenko ¹

¹ UPMC Sorbonne universités, institut de mathématiques de Jussieu, 4, place Jussieu, 75252 Paris cedex 05, France

Comptes Rendus. Mathématique, Volume 349 (2011) no. 21-22, pp. 1131-1134.

Abstract
Résumé

We prove the following conjecture due to Bryant Mathews (2008). Let Q be the orthogonal grassmannian of totally isotropic i-planes of a non-degenerate quadratic form q over an arbitrary field (where i is an integer satisfying $1 ⩽ i ⩽ (\dim q) / 2$ ). If the degree of each closed point on Q is divisible by $2^{i}$ and the Witt index of q over the function field of Q is equal to i, then the variety Q is 2-incompressible.

Nous démontrons la conjecture ci-dessous due à Bryant Mathews (2008). Soit Q la grassmannienne orthogonale des i-plans totalement isotropes dʼune forme quadratique non dégénérée q sur un corps arbitraire (où i est un entier satisfaisant $1 ⩽ i ⩽ (\dim q) / 2$ ). Si le degré de tout point fermé sur Q est divisible par $2^{i}$ et lʼindice de Witt de la forme q au-dessus du corps des fonctions de Q est égal à i, alors la variété Q est 2-incompressible.

Received: 2011-07-09
Accepted: 2011-10-07
Published online: 2011-10-18

DOI: 10.1016/j.crma.2011.10.004

Author's affiliations:

Nikita A. Karpenko ¹

¹ UPMC Sorbonne universités, institut de mathématiques de Jussieu, 4, place Jussieu, 75252 Paris cedex 05, France

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     title = {Incompressibility of orthogonal grassmannians},
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     year = {2011},
     doi = {10.1016/j.crma.2011.10.004},
     language = {en},
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Nikita A. Karpenko. Incompressibility of orthogonal grassmannians. Comptes Rendus. Mathématique, Volume 349 (2011) no. 21-22, pp. 1131-1134. doi : 10.1016/j.crma.2011.10.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.10.004/

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