English

Mixed modular perverse sheaves on affine flag varieties and Koszul duality

Representation Theory 2025-09-16 v2

Abstract

Under some technical assumptions, and building on joint work with Bezrukavnikov, we prove a multiplicity formula for indecomposable tilting perverse sheaves on affine flag varieties, with coefficients in a field of characteristic pp, in terms of pp-Kazhdan--Lusztig polynomials. Under the same assumptions, we also explain the construction of a "degrading functor" relating mixed modular perverse sheaves (as defined in joint work with Achar) on such varieties to ordinary perverse sheaves.

Keywords

Cite

@article{arxiv.2411.01869,
  title  = {Mixed modular perverse sheaves on affine flag varieties and Koszul duality},
  author = {Simon Riche},
  journal= {arXiv preprint arXiv:2411.01869},
  year   = {2025}
}

Comments

v1: 34 pages. Content essentially extracted from arXiv:2206.03738 to be published as a separate paper. v2: 38 pages. Minor corrections. Final version, to appear in Revista de la UMA