no. 21-22
Algebra/Algebraic Geometry
Incompressibility of orthogonal grassmannians
[Incompressibilité de grassmanniennes orthogonales]

Présenté par : Claire Voisin

Karpenko, Nikita A.1
1 UPMC Sorbonne universités, institut de mathématiques de Jussieu, 4, place Jussieu, 75252 Paris cedex 05, France
Comptes Rendus. Mathématique, Tome 349 (2011) no. 21-22, pp. 1131-1134.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.10.004
Karpenko, Nikita A. 1

1 UPMC Sorbonne universités, institut de mathématiques de Jussieu, 4, place Jussieu, 75252 Paris cedex 05, France 
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Karpenko, Nikita A. Incompressibility of orthogonal grassmannians. Comptes Rendus. Mathématique, Tome 349 (2011) no. 21-22, pp. 1131-1134. doi : 10.1016/j.crma.2011.10.004. http://www.numdam.org/articles/10.1016/j.crma.2011.10.004/

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