Gerbes for trigonalizable group schemes
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918132496465920 |
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| author | Olander, Noah Olsson, Martin |
| author_facet | Olander, Noah Olsson, Martin |
| contents | We prove that smooth, separated Deligne--Mumford stacks in mixed characteristic with quasi-projective coarse moduli space are global quotient stacks and satisfy the resolution property. This builds on work of Kresch and Vistoli and of Bragg, Hall, and Matthur which proves the case when the stack is over a base field, as well as work of Gabber and de Jong which proves the same holds for a $μ_n$-gerbe over a scheme with an ample line bundle. The key technical input is a result that gerbes banded by so-called trigonalizable group schemes admit faithful vector bundles and are quotient stacks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21218 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gerbes for trigonalizable group schemes Olander, Noah Olsson, Martin Algebraic Geometry We prove that smooth, separated Deligne--Mumford stacks in mixed characteristic with quasi-projective coarse moduli space are global quotient stacks and satisfy the resolution property. This builds on work of Kresch and Vistoli and of Bragg, Hall, and Matthur which proves the case when the stack is over a base field, as well as work of Gabber and de Jong which proves the same holds for a $μ_n$-gerbe over a scheme with an ample line bundle. The key technical input is a result that gerbes banded by so-called trigonalizable group schemes admit faithful vector bundles and are quotient stacks. |
| title | Gerbes for trigonalizable group schemes |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2508.21218 |