p-adic Borel extension for local Shimura varieties
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915831843127296 |
|---|---|
| author | Oswal, Abhishek Pappas, Georgios |
| author_facet | Oswal, Abhishek Pappas, Georgios |
| contents | We show that the moduli spaces of Scholze's $p$-adic shtukas with framing satisfy a $p$-adic rigid analytic version of Borel's extension theorem. In particular, this holds for local Shimura varieties, for all local Shimura data $(G,[b],\{μ\})$, even for exceptional groups $G$, and extends work of Oswal-Shankar-Zhu-Patel who proved a $p$-adic Borel extension property for Rapoport-Zink spaces. As a corollary, we deduce that all these spaces satisfy a $p$-adic rigid analytic version of Brody hyperbolicity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_14109 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | p-adic Borel extension for local Shimura varieties Oswal, Abhishek Pappas, Georgios Number Theory Algebraic Geometry We show that the moduli spaces of Scholze's $p$-adic shtukas with framing satisfy a $p$-adic rigid analytic version of Borel's extension theorem. In particular, this holds for local Shimura varieties, for all local Shimura data $(G,[b],\{μ\})$, even for exceptional groups $G$, and extends work of Oswal-Shankar-Zhu-Patel who proved a $p$-adic Borel extension property for Rapoport-Zink spaces. As a corollary, we deduce that all these spaces satisfy a $p$-adic rigid analytic version of Brody hyperbolicity. |
| title | p-adic Borel extension for local Shimura varieties |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2502.14109 |