Free-monodromic mixed tilting sheaves on flag varieties

Pramod N Achar (1) , Shotaro Makisumi (2) , Simon N Riche (3, 4) , Geordie N Williamson (5, 6)

1 LSU Mathematics - Department of Mathematics [Baton Rouge]
2 Department of Mathematics [Stanford]
3 INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques
4 LMBP - Laboratoire de Mathématiques Blaise Pascal
5 The University of Sydney
6 MPIM - Max Planck Institute for Mathematics

In this paper we propose a construction of a monoidal category of "free-monodromic" tilting perverse sheaves on (Kac-Moody) flag varieties in the setting of the "mixed modular derived category" introduced by the first and third authors. This category shares most of the properties of their counterpart in characteristic 0, defined by Bezrukavnikov-Yun using certain pro-objects in triangulated categories. This construction is the main new ingredient in the forthcoming construction of a "modular Koszul duality" equivalence for constructible sheaves on flag varieties.

Domaines: Mathématiques [math]

Pramod N Achar, Shotaro Makisumi, Simon N Riche, Geordie N Williamson. Free-monodromic mixed tilting sheaves on flag varieties. 2017. ⟨hal-01492489⟩