Free-Monodromic Mixed Tilting Sheaves on Flag Varieties
Abstract
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 0 , defined by Bezrukavnikov–Yun using certain pro-objects in triangulated categories. This construction is the main new ingredient in the construction of a “modular Koszul duality” equivalence for constructible sheaves on flag varieties, see [J. Amer. Math. Soc. 32 (2019), no. 1, 261–310, DOI 10.1090/jams/905. MR 3868004 ].
// Source
Authors: Pramod N. Achar, Shotaro Makisumi, Simon Riche, Geordie Williamson
Institutions: The University of Sydney, Stanford University, Centre National de la Recherche Scientifique, Louisiana State University, Max Planck Institute for Mathematics, Laboratoire de Mathématiques Blaise Pascal, Institut National des Sciences Mathématiques et de leurs Interactions