Modular perverse sheaves  on flag varieties I:  tilting and parity sheaves

Achar, Pramod N.; Riche, Simon

doi:10.24033/asens.2284

Geodesic

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Modular perverse sheaves on flag varieties I: tilting and parity sheaves
[Faisceaux pervers modulaires sur les variétés de drapeaux I : faisceaux basculants et faisceaux à parité]

Achar, Pramod N. ; Riche, Simon

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 49 (2016) no. 2, pp. 325-370.

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Abstract (VO)
Résumé

In this paper we prove that the category of parity complexes on the flag variety of a complex connected reductive group $G$ is a “graded version” of the category of tilting perverse sheaves on the flag variety of the dual group $\overset{ˇ}{G}$ , for any field of coefficients whose characteristic is good for $G$ . We derive some consequences on Soergel's modular category $𝒪$ , and on multiplicities and decomposition numbers in the category of perverse sheaves.

Dans cet article nous démontrons que la catégorie des complexes à parité sur la variété de drapeaux d'un groupe réductif complexe connexe $G$ est une « version graduée » de la catégorie des faisceaux pervers basculants sur la variété de drapeaux du groupe dual $\overset{ˇ}{G}$ , pour tout corps de coefficients dont la caractéristique est bonne pour $G$ . Nous en déduisons des conséquences sur la catégorie $𝒪$ modulaire de Soergel, et sur le calcul des multiplicités et des nombres de décomposition dans la catégorie des faisceaux pervers.

MR Zbl

DOI : 10.24033/asens.2284

Classification : 14M15; 14F05, 20G40.
Keywords: Flag varieties, reductive algebraic groups, perverse sheaves, parity sheaves, Soergel bimodules, quasi-hereditary categories, modular reduction.
Mots-clés : Variétés de drapeaux, groupes algébriques réductifs, faisceaux pervers, faisceaux à parité, bimodules de Soergel, catégories quasi-héréditaires, réduction modulaire.

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     author = {Achar, Pramod N. and Riche, Simon},
     title = {Modular perverse sheaves  on flag varieties {I:}  tilting and parity sheaves},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {325--370},
     publisher = {Soci\'et\'e Math\'ematique de France. Tous droits r\'eserv\'es},
     volume = {Ser. 4, 49},
     number = {2},
     year = {2016},
     doi = {10.24033/asens.2284},
     mrnumber = {3481352},
     zbl = {1386.14178},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.24033/asens.2284/}
}

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Achar, Pramod N.; Riche, Simon. Modular perverse sheaves  on flag varieties I:  tilting and parity sheaves. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 49 (2016) no. 2, pp. 325-370. doi : 10.24033/asens.2284. http://geodesic.mathdoc.fr/articles/10.24033/asens.2284/

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