Derived categories and Deligne-Lusztig varieties II - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Annals of Mathematics Année : 2017

Derived categories and Deligne-Lusztig varieties II

Résumé

This paper is a continuation and a completion of [BoRo1]. We extend the Jordan decomposition of blocks: we show that blocks of finite groups of Lie type in non-describing characteristic are Morita equivalent to blocks of subgroups associated to isolated elements of the dual group. The key new result is the invariance of the part of the cohomology in a given modular series of Deligne-Lusztig varieties associated to a given Levi subgroup, under certain variations of parabolic subgroups. We also show that the equivalence arises from a splendid Rickard equivalence. Even in the setting of [BoRo1], the finer homotopy equivalence was unknown. As a consequence, the equivalence preserves defect groups and categories of subpairs. We finally determine when Deligne-Lusztig induced representations of tori generate the derived category of representations.
Fichier principal
Vignette du fichier
cdvdl-version-finale.pdf (508.46 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-01228904 , version 1 (14-11-2015)
hal-01228904 , version 2 (19-11-2015)
hal-01228904 , version 3 (29-09-2016)

Identifiants

Citer

Cédric Bonnafé, Jean-François Dat, Raphaël Rouquier. Derived categories and Deligne-Lusztig varieties II. Annals of Mathematics, 2017, 185 (2), pp.609-670. ⟨10.4007/annals.2017.185.2.5⟩. ⟨hal-01228904v3⟩
295 Consultations
174 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More