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arXiv · 2109.13718

Height functions on Hecke orbits and the generalised Andr\'e-Pink-Zannier conjecture

Rodolphe Richard·Andrei Yafaev
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Abstract

We introduce and study the notion of a generalised Hecke orbit in a Shimura variety. We define a height function on such an orbit and study its properties. We obtain a lower bounds for the size of Galois orbits of points in a generalised Hecke orbit in terms of these height, assuming a version of the Mumford-Tate conjecture. We then use it to prove the generalised Andr\'e-Pink-Zannier conjecture under this assumption by implementing the Pila-Zannier strategy.

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BibTeXRIS

Rodolphe Richard, Andrei Yafaev. 2021-09-28. Height functions on Hecke orbits and the generalised Andr\'e-Pink-Zannier conjecture. https://arxiv.org/abs/2109.13718

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