On montre que l’algorithme de Braden-MacPherson calcule les fibres des faisceaux de parité. On en déduit que l’algorithme de Braden-MacPherson peut être utilisé pour calculer les caractères des modules basculants pour les groupes algébriques. Finalement, on montre que le lieu -lisse d’une variété de Schubert coïncide avec son lieu rationnellement lisse, si le graphe de Bruhat sous-jacent satisfait une condition dite GKM.
We show that the Braden-MacPherson algorithm computes the stalks of parity sheaves. As a consequence we deduce that the Braden-MacPherson algorithm may be used to calculate the characters of tilting modules for algebraic groups and show that the -smooth locus of a (Kac-Moody) Schubert variety coincides with the rationally smooth locus, if the underlying Bruhat graph satisfies a GKM-condition.
@article{AIF_2014__64_2_489_0,
author = {Fiebig, Peter and Williamson, Geordie},
title = {Parity sheaves, moment graphs and the $p$-smooth locus of Schubert varieties},
journal = {Annales de l'Institut Fourier},
volume = {64},
year = {2014},
pages = {489-536},
doi = {10.5802/aif.2856},
zbl = {06387283},
mrnumber = {3330913},
language = {en},
url = {http://dml.mathdoc.fr/item/AIF_2014__64_2_489_0}
}
Fiebig, Peter; Williamson, Geordie. Parity sheaves, moment graphs and the $p$-smooth locus of Schubert varieties. Annales de l'Institut Fourier, Tome 64 (2014) pp. 489-536. doi : 10.5802/aif.2856. http://gdmltest.u-ga.fr/item/AIF_2014__64_2_489_0/
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