Relying on recent advances in the theory of motives we develop a general formalism for derived categories of motives with \({\mathbf{Q}}\)-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.

中文翻译：

---

Witt 矢量仿射旗品种的 Tate 动机

依靠动机理论的最新进展，我们为具有\({\mathbf{Q}}\) -系数在完美\(\infty \) -prestacks上的派生动机类别开发了一般形式主义。我们构造了 Grothendieck 的六个函子，用于在有限表示的完美（ind-）方案上的动机。遵循 Soergel-Wendt 的思想，这被用来研究分层 Tate 动机在 Witt 向量部分仿射标志变体上的基本性质。作为一个应用，我们在此设置中对 Witt 向量仿射 Grassmannians 的 Zhu 几何 Satake 等价进行了动机改进。