[Incompressibilité de grassmanniennes orthogonales]
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 ). Si le degré de tout point fermé sur Q est divisible par 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 ). If the degree of each closed point on Q is divisible by and the Witt index of q over the function field of Q is equal to i, then the variety Q is 2-incompressible.
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@article{CRMATH_2011__349_21-22_1131_0,
author = {Nikita A. Karpenko},
title = {Incompressibility of orthogonal grassmannians},
journal = {Comptes Rendus. Math\'ematique},
pages = {1131--1134},
publisher = {Elsevier},
volume = {349},
number = {21-22},
year = {2011},
doi = {10.1016/j.crma.2011.10.004},
language = {en},
}
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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