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arXiv · 2502.14109

p-adic Borel extension for local Shimura varieties

Abhishek Oswal·Georgios Pappas
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Abstract

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 $(G,[b],\{\mu\})$, 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.

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Abhishek Oswal, Georgios Pappas. 2025-02-19. p-adic Borel extension for local Shimura varieties. https://doi.org/10.1017/fms.2026.10188

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