Tate motives on Witt vector affine flag varieties

Author:

Richarz Timo,Scholbach Jakob

Abstract

AbstractRelying on recent advances in the theory of motives we develop a general formalism for derived categories of motives with $${\mathbf{Q}}$$ Q -coefficients on perfect $$\infty $$ -prestacks. We construct Grothendieck’s six functors for motives over perfect (ind-)schemes perfectly of finite presentation. Following ideas of Soergel–Wendt, this is used to study basic properties of stratified Tate motives on Witt vector partial affine flag varieties. As an application we give a motivic refinement of Zhu’s geometric Satake equivalence for Witt vector affine Grassmannians in this set-up.

Funder

Westfälische Wilhelms-Universität Münster

Publisher

Springer Science and Business Media LLC

Subject

General Physics and Astronomy,General Mathematics

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