Contraction par Frobenius de G-modules
Annales de l'Institut Fourier, Tome 61 (2011) no. 6, p. 2507-2542
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.
DOI : https://doi.org/10.5802/aif.2681
Classification:  14M15,  13A35,  17B10,  20G05,  20G10
Mots clés: scindage de Frobenius, variété des drapeaux, variété de Schubert, algèbre des distributions
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {61},
     number = {6},
     year = {2011},
     pages = {2507-2542},
     doi = {10.5802/aif.2681},
     mrnumber = {2976319},
     zbl = {1257.14035},
     language = {fr},
     url = {http://http://www.numdam.org/item/AIF_2011__61_6_2507_0}
}
Gros, Michel; Kaneda, Masaharu. Contraction par Frobenius de $G$-modules. Annales de l'Institut Fourier, Tome 61 (2011) no. 6, pp. 2507-2542. doi : 10.5802/aif.2681. http://www.numdam.org/item/AIF_2011__61_6_2507_0/

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