Compact approximation and descent for algebraic stacks
Algebraic Geometry
2025-05-01 v1
Abstract
This work focuses on approximation and generation for the derived category of complexes with quasi-coherent cohomology on algebraic stacks. Our methods establish that approximation by compact objects descends along covers that are quasi-finite and flat. This generalizes a result of Lipman--Neeman for schemes and extends a related result known for algebraic spaces. We also study the behavior of generation under the derived pushforward and pullback of a morphism between algebraic stacks.
Cite
@article{arxiv.2504.21125,
title = {Compact approximation and descent for algebraic stacks},
author = {Jack Hall and Alicia Lamarche and Pat Lank and Fei Peng},
journal= {arXiv preprint arXiv:2504.21125},
year = {2025}
}
Comments
v1, comments welcome!