A note on quasi-perfect morphisms
Algebraic Geometry
2026-03-18 v3
Abstract
This note is concerned with quasi-perfect morphisms between Noetherian algebraic spaces. In particular, we study the local behavior of quasi-perfect proper morphisms. We show that quasi-perfectness of a proper morphism can be detected at the \'{e}tale local rings of points of the target, as well as their completions and (strict) Henselizations. As a corollary, we obtain that the locus of points where a proper morphism is quasi-perfect is Zariski open.
Cite
@article{arxiv.2508.10845,
title = {A note on quasi-perfect morphisms},
author = {Timothy De Deyn and Pat Lank and Kabeer Manali Rahul},
journal= {arXiv preprint arXiv:2508.10845},
year = {2026}
}
Comments
moved regularity characterization to appendix, comments welcome!