Gros, Michel; Kaneda, Masaharu
Contraction par Frobenius de G-modules
Annales de l'institut Fourier, Tome 61 (2011) no. 6 , p. 2507-2542
MR 2976319 | Zbl 1257.14035
doi : 10.5802/aif.2681
URL stable : http://www.numdam.org/item?id=AIF_2011__61_6_2507_0

Classification:  14M15,  13A35,  17B10,  20G05,  20G10
Mots clés: scindage de Frobenius, variété des drapeaux, variété de Schubert, algèbre des distributions
Soit G un groupe algébrique semi-simple simplement connexe défini sur un corps algébriquement clos 𝕜 de caractéristique positive. Nous donnons une nouvelle preuve de l’existence d’un scindage de Frobenius de la variété des drapeaux de G ainsi que de la nature G-équivariante de celui-ci. L’outil principal est un scindage de l’endomorphisme de Frobenius défini sur toute l’algèbre des distributions de G qui permet de « détordre » la structure des G-modules.
Let G be a simply connected semisimple algebraic group over an algebraically closed field 𝕜 of positive characteristic. We will give a new proof of the Frobenius splitting of the flag variety of G and of its G-equivariant nature. The key tool is a newly found splitting of the Frobenius endomorphism on the algebra of distributions of G allowing us to “untwist” the structure of G-modules.

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