Parity sheaves, moment graphs and the p-smooth locus of Schubert varieties
Annales de l'Institut Fourier, Volume 64 (2014) no. 2, p. 489-536
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.
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.
Received : 2011-11-28
Revised : 2013-02-08
Accepted : 2013-04-22
DOI : https://doi.org/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
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {64},
     number = {2},
     year = {2014},
     pages = {489-536},
     doi = {10.5802/aif.2856},
     zbl = {06387283},
     mrnumber = {3330913},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2014__64_2_489_0}
}
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/item/AIF_2014__64_2_489_0/

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