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math.NT2021
Generalised André-Pink-Zannier Conjecture for Shimura varieties of abelian type
Rodolphe Richard, Andrei Yafaev
In this paper, we prove the generalised André-Pink-Zannier conjecture (an important case of the Zilber-Pink conjecture) for all Shimura varieties of abelian type. Questions of this…
math.NT2021
Height functions on Hecke orbits and the generalised André-Pink-Zannier conjecture
Rodolphe Richard, Andrei Yafaev
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…
math.NT2021★ 2 cited
Manin-Mumford in arithmetic pencils
Gregorio Baldi, Rodolphe Richard, Emmanuel Ullmo
We obtain a refinement of Manin-Mumford (Raynaud's Theorem) for abelian schemes over some ring of integers. Torsion points are replaced by special 0-cycles, that is reductions modu…