Tate motives on Witt vector affine flag varieties

Timo Richarz ^[1] ; Jakob Scholbach ^[2]
1. [1] TU Darmstadt, Alemania
2. [2] WWU Münster, Alemania
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 27, Nº. 3, 2021
Idioma: inglés
DOI: 10.1007/s00029-021-00665-y
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Resumen
- Relying on recent advances in the theory of motives we develop a general formalism for derived categories of motives with Q-coefficients on perfect ∞-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.