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arXiv · 2506.06932

Towards a p-adic nowhere density conjecture of Hecke Orbits

Yu Fu
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Abstract

We propose a conjecture on the $p$-adic nowhere density of the Hecke orbit of subvarieties of Hodge type Shimura varieties. By investigating the monodromy of $p$-adic Galois representations associated with points on such Shimura varieties, we prove that the locus in a formal $\mathcal{O}_K$-neighborhood of a mod $p$ point that has large monodromy is open dense, where $K$ is a totally ramified finite extension of $\breve{\mathbb{Q}}_p.$

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Yu Fu. 2025-06-07. Towards a p-adic nowhere density conjecture of Hecke Orbits. https://arxiv.org/abs/2506.06932

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