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A characteristic p analogue of the Andr\'e--Pink--Zannier conjecture
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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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Cited by 1 Pith paper
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Unlikely intersections in Shimura varieties and beyond: a survey
A survey of unlikely intersections in pure Shimura varieties, covering Andre-Oort, Andre-Pink-Zannier, Zilber-Pink, and the Pila-Zannier strategy.
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