Tate motives on Witt vector affine flag varieties

Abstract

Relying on recent advances in the theory of motives we develope a general formalism for derived categories of motives with Q-coefficients on perfect (ind-)schemes. As an application we give a motivic refinement of Zhu's geometric Satake equivalence for Witt vector affine Grassmannians in this set-up. Contents 1. Introduction 1 2. Motives on perfect (ind-)schemes 4 3. Stratified Tate motives for perfect ind-schemes 10 4. Motives on Witt vector affine flag varieties 12 5. The motivic Satake equivalence 17 References 21