English

Rational motives on pro-algebraic stacks

Algebraic Geometry 2025-10-30 v4

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 66-functor formalism for certain classes of morphisms. On pro-schemes, we show that this 66-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

R2 v1 2026-06-28T15:10:48.372Z