On the geometric connected components of moduli spaces of p-adic shtukas and local Shimura varieties
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866918119566475264 |
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| author | Gleason, Ian |
| author_facet | Gleason, Ian |
| contents | We study topological properties of moduli spaces of p-adic shtukas and local Shimura varieties. On one hand, we construct and study the specialization map for moduli spaces of p-adic shtukas at parahoric level whose target is an affine Deligne-Lusztig variety. On the other hand, given a p-adic shtuka datum $(G, b, μ)$, with $G$ unramified over $\mathbb{Q}_p$ and such that $(b, μ)$ is HN-irreducible, we determine the set of geometric connected components of infinite level moduli spaces of p-adic shtukas. In other words, we understand $π_0(\mathrm{Sht}_{(G,b,μ,\infty)} \times \mathrm{Spd} \mathbb{C}_p)$ with its right $G(\mathbb{Q}_p) \times G_b (\mathbb{Q}p ) \times W_E$ -action. As a corollary, we prove new cases of a conjecture of Rapoport and Viehmann. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_03579 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On the geometric connected components of moduli spaces of p-adic shtukas and local Shimura varieties Gleason, Ian Algebraic Geometry Number Theory We study topological properties of moduli spaces of p-adic shtukas and local Shimura varieties. On one hand, we construct and study the specialization map for moduli spaces of p-adic shtukas at parahoric level whose target is an affine Deligne-Lusztig variety. On the other hand, given a p-adic shtuka datum $(G, b, μ)$, with $G$ unramified over $\mathbb{Q}_p$ and such that $(b, μ)$ is HN-irreducible, we determine the set of geometric connected components of infinite level moduli spaces of p-adic shtukas. In other words, we understand $π_0(\mathrm{Sht}_{(G,b,μ,\infty)} \times \mathrm{Spd} \mathbb{C}_p)$ with its right $G(\mathbb{Q}_p) \times G_b (\mathbb{Q}p ) \times W_E$ -action. As a corollary, we prove new cases of a conjecture of Rapoport and Viehmann. |
| title | On the geometric connected components of moduli spaces of p-adic shtukas and local Shimura varieties |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2107.03579 |