Institute of Mathematics

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.