Perfect generation for regular algebraic stacks
Algebraic Geometry
2026-03-25 v3 Commutative Algebra
Category Theory
Abstract
We show that the derived category of complexes with quasi-coherent cohomology on a regular Noetherian algebraic stack with quasi-finite diagonal is generated by a single perfect complex. In the concentrated case, the category is singly compactly generated. Key ingredients in the proofs include gluing generators along recollement and the use of suitable filtrations and presentations of the algebraic stack.
Cite
@article{arxiv.2601.04053,
title = {Perfect generation for regular algebraic stacks},
author = {Pat Lank},
journal= {arXiv preprint arXiv:2601.04053},
year = {2026}
}
Comments
Removed separatedness, sharpened a few proofs, and title change; comments welcome!