Descending strong generation in algebraic geometry
Algebraic Geometry
2025-02-13 v1 Commutative Algebra
Abstract
We formalize the main approach for showing Zariski descent-type statements for strong generation of triangulated categories associated to algebro-geometric objects. This recovers various known statements in the literature. As applications we show that strong generation for the singularity category of a Noetherian separated scheme is Zariski local and obtain a strong generation result for the bounded derived category of a Noetherian concentrated algebraic stacks with finite diagonal.
Cite
@article{arxiv.2502.08629,
title = {Descending strong generation in algebraic geometry},
author = {Timothy De Deyn and Pat Lank and Kabeer Manali Rahul},
journal= {arXiv preprint arXiv:2502.08629},
year = {2025}
}
Comments
v1, comments welcome!