Perverse sheaves on affine flag varieties and coherent sheaves on the dual Steinberg variety

Time:Fri., 4:00-5:00pm, Oct.14,2022

Venue:Zoom Meeting ID: 271 534 5558 Passcode: YMSC

Speaker:Prof. Simon Riche (Université Clermont Auvergne)


We will report on an ongoing project with R. Bezrukavnikov and L. Rider which aims at constructing an equivalence of categories lifting to the categorical level the comparison between the two natural geometric realizations of the affine Hecke algebra of a reductive group: one in terms of constructible sheaves on the associated affine flag variety, and one in terms of coherent sheaves on the Steinberg variety of the Langlands dual group. Such a construction has been obtained by Bezrukavnikov for coefficients in characteristic 0, and the case we now want to consider is that of positive-characteristic coefficients. As of now we have obtained a description of perverse sheaves on the affine flag variety in terms of some "Soergel bimodules", which we will use to related these objects to the dual side. As a first application, we are able to compute stalks of tilting perverse sheaves on the affine flag variety in terms of p-Kazhdan-Lusztig polynomials.


Simon Riche, Full Professor, at Université Clermont Auvergne (Clermont–Ferrand, France)

DATESeptember 29, 2022
Related News
    • 0

      The perverse filtration of abelian fibrations via Fourier-Mukai

      AbstractThe perverse (Leray) filtration captures key topological information of algebraic maps. Recent studies of integrable systems (e.g. Hitchin system, Beauville-Mukai system) suggests two common features of the perverse filtration of abelian fibrations:1) the perverse filtration is multiplicative with respect to the cup product;2) the perversity of tautological classes is governed by the Ch...

    • 1

      A Noether-Lefschetz type theorem for spectral varieties with applications

      AbstractIn this talk, we will discuss spectral variety and related moduli spaces of Higgs pairs on surfaces. We will first introduce the geometry of moduli of Higgs pairs and the spectral varieties. Indeed, we will talk about the Noether-Lefschetz type problems and the Picard schemes of the spectral varieties. If time permits, the Picard group of generic (very general) spectral varieties and it...