A note on quasi-perfect morphisms
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908891839725568 |
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| author | De Deyn, Timothy Lank, Pat Rahul, Kabeer Manali |
| author_facet | De Deyn, Timothy Lank, Pat Rahul, Kabeer Manali |
| contents | 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 étale 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10845 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on quasi-perfect morphisms De Deyn, Timothy Lank, Pat Rahul, Kabeer Manali Algebraic Geometry 14A30 (primary), 13D09, 14B05, 18G80 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 étale 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. |
| title | A note on quasi-perfect morphisms |
| topic | Algebraic Geometry 14A30 (primary), 13D09, 14B05, 18G80 |
| url | https://arxiv.org/abs/2508.10845 |