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Compositio Mathematica

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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 lower bounds for the sizes of Galois orbits of points in a generalised Hecke orbit in terms of this height function, assuming the ‘weakly adelic Mumford–Tate hypothesis’ and prove the generalised André–Pink–Zannier conjecture under this assumption, using Pila–Zannier strategy.

Compositio Mathematica

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Height functions on Hecke orbits and the generalised André–Pink–Zannier conjecture

Compositio Mathematica

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Height functions on Hecke orbits and the generalised André–Pink–Zannier conjecture