no. 2
Parity sheaves, moment graphs and the p-smooth locus of Schubert varieties
[Faisceaux de parité, graphes de moment et lieu p-lisse des variétés de Schubert]
Fiebig, Peter1 ; Williamson, Geordie2
1 Emmy-Noether-Zentrum FAY Erlangen-Nürnberg Cauerstr. 11 91058 Erlangen (Germany)
2 Max-Planck-Institut für Mathematik Vivatsgasse 7 53111 Bonn (Germany)
Annales de l'Institut Fourier, Tome 64 (2014) no. 2, pp. 489-536.

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 p-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 p-smooth locus of a (Kac-Moody) Schubert variety coincides with the rationally smooth locus, if the underlying Bruhat graph satisfies a GKM-condition.

DOI : 10.5802/aif.2856
Classification : 20C20, 22E47, 55N33, 55N91, 14M15
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

1 Emmy-Noether-Zentrum FAY Erlangen-Nürnberg Cauerstr. 11 91058 Erlangen (Germany)
2 Max-Planck-Institut für Mathematik Vivatsgasse 7 53111 Bonn (Germany) 
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Fiebig, Peter; Williamson, Geordie. Parity sheaves, moment graphs and the $p$-smooth locus of Schubert varieties. Annales de l'Institut Fourier, Tome 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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