Rational motives on pro-algebraic stacks
Algebraic Geometry
2025-10-30 v4
Abstract
We define an -category of rational motives for inverse limits of algebraic stacks, so-called pro-algebraic stacks. We show that it admits a -functor formalism for certain classes of morphisms. On pro-schemes, we show that this -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.
Keywords
Cite
@article{arxiv.2403.03596,
title = {Rational motives on pro-algebraic stacks},
author = {Can Yaylali},
journal= {arXiv preprint arXiv:2403.03596},
year = {2025}
}
Comments
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