Unipotent morphisms
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866914528921387008 |
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| author | Bragg, Daniel Hall, Jack Mathur, Siddharth |
| author_facet | Bragg, Daniel Hall, Jack Mathur, Siddharth |
| contents | We introduce the theory of unipotent morphisms of algebraic stacks and prove a surprising local to global principle for a class of vector bundles. Two sample applications of our methods are the following: (1) a unipotent analogue of Gabber's Theorem for torsion $\mathbf{G}_m$-gerbes and (2) smooth Deligne-Mumford stacks with quasi-projective coarse spaces satisfy the resolution property in positive characteristic. Our main tool is a descent result for flags, which we prove using results of Schäppi. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_15041 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Unipotent morphisms Bragg, Daniel Hall, Jack Mathur, Siddharth Algebraic Geometry 14A20 We introduce the theory of unipotent morphisms of algebraic stacks and prove a surprising local to global principle for a class of vector bundles. Two sample applications of our methods are the following: (1) a unipotent analogue of Gabber's Theorem for torsion $\mathbf{G}_m$-gerbes and (2) smooth Deligne-Mumford stacks with quasi-projective coarse spaces satisfy the resolution property in positive characteristic. Our main tool is a descent result for flags, which we prove using results of Schäppi. |
| title | Unipotent morphisms |
| topic | Algebraic Geometry 14A20 |
| url | https://arxiv.org/abs/2110.15041 |