The étale local structure of algebraic stacks
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866916673352630272 |
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| author | Alper, Jarod Hall, Jack Rydh, David |
| author_facet | Alper, Jarod Hall, Jack Rydh, David |
| contents | We prove that an algebraic stack with affine stabilizers over an arbitrary base is étale-locally a quotient stack around any point with a linearly reductive stabilizer. This generalizes earlier work by the authors of this article (stacks over algebraically closed fields) and by Abramovich, Olsson and Vistoli (stacks with finite inertia). In addition, we prove a number of foundational results, which are new even over a field. These include various coherent completeness and effectivity results for adic sequences of algebraic stacks. Finally, we give several applications of our results and methods, such as structure theorems for linearly reductive group schemes and generalizations to the relative setting of Sumihiro's theorem on torus actions and Luna's étale slice theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1912_06162 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | The étale local structure of algebraic stacks Alper, Jarod Hall, Jack Rydh, David Algebraic Geometry 14D23 (Primary), 14L15, 14L24, 14L30 (Secondary) We prove that an algebraic stack with affine stabilizers over an arbitrary base is étale-locally a quotient stack around any point with a linearly reductive stabilizer. This generalizes earlier work by the authors of this article (stacks over algebraically closed fields) and by Abramovich, Olsson and Vistoli (stacks with finite inertia). In addition, we prove a number of foundational results, which are new even over a field. These include various coherent completeness and effectivity results for adic sequences of algebraic stacks. Finally, we give several applications of our results and methods, such as structure theorems for linearly reductive group schemes and generalizations to the relative setting of Sumihiro's theorem on torus actions and Luna's étale slice theorem. |
| title | The étale local structure of algebraic stacks |
| topic | Algebraic Geometry 14D23 (Primary), 14L15, 14L24, 14L30 (Secondary) |
| url | https://arxiv.org/abs/1912.06162 |