A characteristic p analogue of the André--Pink--Zannier conjecture

2025/05/18 by Yeuk Hay Joshua Lam, Lam, Yeuk Hay Joshua, Ananth N. Shankar +1 · 2 citations
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.2505.12521

Abstract

We investigate the analogue of the André--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.

Cited by

• Logarithmic Dieudonné theory and overconvergent extensions
• Finiteness of function field-valued points on exceptional Shimura varieties

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