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.
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.
Keywords: Modular representation theory, equivariant cohomology, moment graphs, constructible sheaves, tilting modules, Schubert varieties, $p$-smooth locus
Mot clés : théorie des représentations modulaires, cohomologie équivariante, graphes de moment, faisceaux constructibles, modules basculants, variétés de Schubert, lieu $p$-lisse
Fiebig, Peter 1; Williamson, Geordie 2
@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}, pages = {489--536}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {64}, number = {2}, year = {2014}, doi = {10.5802/aif.2856}, mrnumber = {3330913}, zbl = {06387283}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2856/} }
TY - JOUR AU - Fiebig, Peter AU - Williamson, Geordie TI - Parity sheaves, moment graphs and the $p$-smooth locus of Schubert varieties JO - Annales de l'Institut Fourier PY - 2014 SP - 489 EP - 536 VL - 64 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2856/ DO - 10.5802/aif.2856 LA - en ID - AIF_2014__64_2_489_0 ER -
%0 Journal Article %A Fiebig, Peter %A Williamson, Geordie %T Parity sheaves, moment graphs and the $p$-smooth locus of Schubert varieties %J Annales de l'Institut Fourier %D 2014 %P 489-536 %V 64 %N 2 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2856/ %R 10.5802/aif.2856 %G en %F 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, Volume 64 (2014) no. 2, pp. 489-536. doi : 10.5802/aif.2856. https://aif.centre-mersenne.org/articles/10.5802/aif.2856/
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