Let be a simply connected semisimple algebraic group over an algebraically closed field of positive characteristic. We will give a new proof of the Frobenius splitting of the flag variety of and of its -equivariant nature. The key tool is a newly found splitting of the Frobenius endomorphism on the algebra of distributions of allowing us to “untwist” the structure of -modules.
Soit un groupe algébrique semi-simple simplement connexe défini sur un corps algébriquement clos de caractéristique positive. Nous donnons une nouvelle preuve de l’existence d’un scindage de Frobenius de la variété des drapeaux de ainsi que de la nature -équivariante de celui-ci. L’outil principal est un scindage de l’endomorphisme de Frobenius défini sur toute l’algèbre des distributions de qui permet de « détordre » la structure des -modules.
Mot clés : scindage de Frobenius, variété des drapeaux, variété de Schubert, algèbre des distributions
Keywords: Frobenius splitting, flag variety, Schubert variety, distribution algebra
@article{AIF_2011__61_6_2507_0, author = {Gros, Michel and Kaneda, Masaharu}, title = {Contraction par {Frobenius} de $G$-modules}, journal = {Annales de l'Institut Fourier}, pages = {2507--2542}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {61}, number = {6}, year = {2011}, doi = {10.5802/aif.2681}, zbl = {1257.14035}, mrnumber = {2976319}, language = {fr}, url = {http://www.numdam.org/articles/10.5802/aif.2681/} }
TY - JOUR AU - Gros, Michel AU - Kaneda, Masaharu TI - Contraction par Frobenius de $G$-modules JO - Annales de l'Institut Fourier PY - 2011 SP - 2507 EP - 2542 VL - 61 IS - 6 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2681/ DO - 10.5802/aif.2681 LA - fr ID - AIF_2011__61_6_2507_0 ER -
%0 Journal Article %A Gros, Michel %A Kaneda, Masaharu %T Contraction par Frobenius de $G$-modules %J Annales de l'Institut Fourier %D 2011 %P 2507-2542 %V 61 %N 6 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2681/ %R 10.5802/aif.2681 %G fr %F AIF_2011__61_6_2507_0
Gros, Michel; Kaneda, Masaharu. Contraction par Frobenius de $G$-modules. Annales de l'Institut Fourier, Volume 61 (2011) no. 6, pp. 2507-2542. doi : 10.5802/aif.2681. http://www.numdam.org/articles/10.5802/aif.2681/
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