Serre functors and local duality for affine quotients
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866916039514652672 |
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| author | Noden, Ivan |
| author_facet | Noden, Ivan |
| contents | The purpose of this short note is to study Serre functors of categories of quasicoherent sheaves on stacks of the form $\mathcal{Y} = \mathrm{Spec} A/G$ where $G$ is a reductive group acting on $\mathrm{Spec} A$ with a unique closed orbit. We show that the Serre functor is given by tensoring with the local cohomology of $ω_\mathcal{Y}$ at the unique closed orbit. Using this description, we develop analogues of the Matlis and local duality theorems for local rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_21290 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Serre functors and local duality for affine quotients Noden, Ivan Algebraic Geometry The purpose of this short note is to study Serre functors of categories of quasicoherent sheaves on stacks of the form $\mathcal{Y} = \mathrm{Spec} A/G$ where $G$ is a reductive group acting on $\mathrm{Spec} A$ with a unique closed orbit. We show that the Serre functor is given by tensoring with the local cohomology of $ω_\mathcal{Y}$ at the unique closed orbit. Using this description, we develop analogues of the Matlis and local duality theorems for local rings. |
| title | Serre functors and local duality for affine quotients |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2605.21290 |