تقرير
Coherently complete algebraic stacks in positive characteristic
| العنوان: | Coherently complete algebraic stacks in positive characteristic |
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| المؤلفون: | Alper, Jarod, Hall, Jack, Lim, David Benjamin |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry, Primary 14F06, 14A20, Secondary 14F08 |
| الوصف: | With the long-term goal of proving local structure theorems of algebraic stacks in positive characteristic near points with reductive (but possibly non-linearly reductive) stabilizer, we conjecture that quotient stacks of the form $[\mathrm{Spec}\, A/G]$, with $G$ reductive and $A^G$ complete local, are coherently complete along the unique closed point. We establish this conjecture in two interesting cases: (1) $A^G$ is artinian and (2) $G$ acts trivially on $\mathrm{Spec}\, A$. We also establish coherent completeness results for graded unipotent group actions. In order to establish these results, we prove a number of foundational statements concerning cohomological and completeness properties of algebraic stacks -- including on how these properties ascend and descend along morphisms. Comment: 35 pages, comments welcome! |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2309.01388 |
| رقم الأكسشن: | edsarx.2309.01388 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |