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arXiv · 2508.10845

A note on quasi-perfect morphisms

Timothy De Deyn·Pat Lank·Kabeer Manali Rahul
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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.

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Timothy De Deyn, Pat Lank, Kabeer Manali Rahul. 2025-08-14. A note on quasi-perfect morphisms. https://arxiv.org/abs/2508.10845

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