On the strongly regular locus of the inertia stack of $\mathrm{Bun}_G$
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913600320307200 |
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| author | Gulotta, Daniel R. |
| author_facet | Gulotta, Daniel R. |
| contents | Let $G$ be a connected reductive group over a finite extension of $\mathbb{Q}_p$. We show that for each $b \in B(G)$, the strongly regular locus of the inertia stack of $\operatorname{Bun}_G^b$ is open in the inertia stack of $\operatorname{Bun}_G$. As a consequence, we extend the computation of Hansen--Kaletha--Weinstein of trace distributions of the cohomology of local shtuka spaces $\mathrm{Sht}_{G,b,μ}$ to non-basic $b$. If $b$ is closed in $B(G,μ)$, or $b$ is basic and has only one specialization in $B(G,μ)$, then we compute the trace distribution of the entire strongly regular locus. In the process, we prove some results on the behavior of characteristic classes under cohomologically smooth pullback. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_17307 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the strongly regular locus of the inertia stack of $\mathrm{Bun}_G$ Gulotta, Daniel R. Number Theory Algebraic Geometry Representation Theory 11S37, 14D24, 11F77, 11F85, 14G45 Let $G$ be a connected reductive group over a finite extension of $\mathbb{Q}_p$. We show that for each $b \in B(G)$, the strongly regular locus of the inertia stack of $\operatorname{Bun}_G^b$ is open in the inertia stack of $\operatorname{Bun}_G$. As a consequence, we extend the computation of Hansen--Kaletha--Weinstein of trace distributions of the cohomology of local shtuka spaces $\mathrm{Sht}_{G,b,μ}$ to non-basic $b$. If $b$ is closed in $B(G,μ)$, or $b$ is basic and has only one specialization in $B(G,μ)$, then we compute the trace distribution of the entire strongly regular locus. In the process, we prove some results on the behavior of characteristic classes under cohomologically smooth pullback. |
| title | On the strongly regular locus of the inertia stack of $\mathrm{Bun}_G$ |
| topic | Number Theory Algebraic Geometry Representation Theory 11S37, 14D24, 11F77, 11F85, 14G45 |
| url | https://arxiv.org/abs/2312.17307 |