Rational motives on pro-algebraic stacks

Abstract

We define an $\infty$-category of rational motives for inverse limits of algebraic stacks, so-called pro-algebraic stacks. We show that it admits a $6$-functor formalism for certain classes of morphisms. On pro-schemes, we show that this $6$-functor formalism is in the sense of Liu-Zheng. This theory yields an approach to the theory of motives for non-representable algebraic stacks and non-finite type morphisms.

Added computation of the motive of the stack of displays. Rewritten introduction, improvement of the proof of Prop. 3.17 and section 3.2.1; 32 pages