Algebra/Algebraic Geometry
Incompressibility of orthogonal grassmannians
Comptes Rendus. Mathématique, Volume 349 (2011) no. 21-22, pp. 1131-1134.

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 $1⩽i⩽(dimq)/2$). If the degree of each closed point on Q is divisible by $2i$ 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 $1⩽i⩽(dimq)/2$). Si le degré de tout point fermé sur Q est divisible par $2i$ 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.

Accepted:
Published online:
DOI: 10.1016/j.crma.2011.10.004
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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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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