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arXiv · 2505.12521

A characteristic p analogue of the Andr\'e--Pink--Zannier conjecture

Yeuk Hay Joshua Lam·Ananth N. Shankar
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Abstract

We investigate the analogue of the Andr\'e--Pink--Zannier conjecture in characteristic $p$. Precisely, we prove it for ordinary function field-valued points with big monodromy, in Shimura varieties of Hodge type. We also prove an algebraic characteristic $p$ analogue of Hecke-equidistribution (as formulated by Mazur) for Shimura varieties of Hodge type. We prove our main results by a global and local analysis of prime-to-$p$ Hecke correspondences, and by showing that Weyl special points are abundant in positive characterstic.

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Yeuk Hay Joshua Lam, Ananth N. Shankar. 2025-05-18. A characteristic p analogue of the Andr\'e--Pink--Zannier conjecture. https://arxiv.org/abs/2505.12521

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