Abstract: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 $\omega_\mathcal{Y}$ at the unique closed orbit. Using this description, we develop analogues of the Matlis and local duality theorems for local rings.
| Comments: | 12 pages |
| Subjects: | Algebraic Geometry (math.AG) |
| Cite as: | arXiv:2605.21290 [math.AG] |
| (or arXiv:2605.21290v2 [math.AG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.21290 arXiv-issued DOI via DataCite |
From: Ivan Noden [view email]
[v1]
Wed, 20 May 2026 15:24:05 UTC (16 KB)
[v2]
Fri, 22 May 2026 13:36:02 UTC (16 KB)
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