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Central motives on parahoric flag varieties

  • Robert Cass

    University of Michigan, Ann Arbor, USA; Claremont McKenna College, USA
    ORCID

  • Thibaud van den Hove

    Max Planck Institute for Mathematics, Bonn, Germany
    ORCID

  • Jakob Scholbach

    Università degli Studi di Padova, Italy
    ORCID
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Abstract

We construct a refinement of Gaitsgory’s central functor for integral motivic sheaves, and show it preserves stratified Tate motives. Towards this end, we develop a reformulation of unipotent motivic nearby cycles, which also works over higher-dimensional bases. We moreover introduce Wakimoto motives and use them to show that our motivic central functor is t-exact. A decategorification of these functors yields a new approach to generic Hecke algebras for general parahorics.

Cite this article

Robert Cass, Thibaud van den Hove, Jakob Scholbach, Central motives on parahoric flag varieties. J. Eur. Math. Soc. (2025), published online first

DOI 10.4171/JEMS/1748