Finiteness of formal pushforwards
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917978610597888 |
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| author | Harbater, David Hartmann, Julia Krashen, Daniel |
| author_facet | Harbater, David Hartmann, Julia Krashen, Daniel |
| contents | Under mild hypotheses, given a scheme $U$ and an open subset $V$ whose complement has codimension at least two, the pushforward of a torsion-free coherent sheaf on $V$ is coherent on $U$. We prove an analog of this result in the context of formal schemes over a complete discrete valuation ring. We then apply this to obtain a result about gluing formal functions, where the patches do not cover the entire scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01504 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finiteness of formal pushforwards Harbater, David Hartmann, Julia Krashen, Daniel Algebraic Geometry Commutative Algebra 14D15, 13F25, 13B35 (primary), 13F40 (secondary) Under mild hypotheses, given a scheme $U$ and an open subset $V$ whose complement has codimension at least two, the pushforward of a torsion-free coherent sheaf on $V$ is coherent on $U$. We prove an analog of this result in the context of formal schemes over a complete discrete valuation ring. We then apply this to obtain a result about gluing formal functions, where the patches do not cover the entire scheme. |
| title | Finiteness of formal pushforwards |
| topic | Algebraic Geometry Commutative Algebra 14D15, 13F25, 13B35 (primary), 13F40 (secondary) |
| url | https://arxiv.org/abs/2502.01504 |