English

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.

Keywords

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!

R2 v1 2026-07-01T04:50:19.438Z