The plectic conjecture over local fields
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866909712480468992 |
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| author | Li-Huerta, Siyan Daniel |
| author_facet | Li-Huerta, Siyan Daniel |
| contents | Using a mixed-characteristic incarnation of fusion, we prove an analog of Nekovář-Scholl's plectic conjecture for local Shimura varieties. We apply this to obtain results on the plectic conjecture for (global) Shimura varieties after restricting to a decomposition group. Along the way, we prove a $p$-adic uniformization theorem for the basic locus of abelian type Shimura varieties at hyperspecial level, which is of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_09962 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The plectic conjecture over local fields Li-Huerta, Siyan Daniel Number Theory Algebraic Geometry Representation Theory 11G18 (Primary) 11F77, 11F41 (Secondary) Using a mixed-characteristic incarnation of fusion, we prove an analog of Nekovář-Scholl's plectic conjecture for local Shimura varieties. We apply this to obtain results on the plectic conjecture for (global) Shimura varieties after restricting to a decomposition group. Along the way, we prove a $p$-adic uniformization theorem for the basic locus of abelian type Shimura varieties at hyperspecial level, which is of independent interest. |
| title | The plectic conjecture over local fields |
| topic | Number Theory Algebraic Geometry Representation Theory 11G18 (Primary) 11F77, 11F41 (Secondary) |
| url | https://arxiv.org/abs/2208.09962 |