3 citations · 12 across the 11 of their papers we have counts for
14 papers
Hybrid Conjecture in a Mixed Shimura variety
Rodolphe Richard, Andrei Yafaev
The authors previously formulated the hybrid conjecture, unifying André-Pink-Zannier and André-Oort conjectures, and proved it in Shimura varieties of abelian type. We study its an…
Heights on 'Hybrid orbits' in Shimura varieties
Rodolphe Richard, Andrei Yafaev
We prove the 'hybrid conjecture' which is a common generalisation of the Andreé-Oort conjecture and the André-Pink-Zannier conjecture, in the case of Shimura varieties of abelian t…
A Common Generalisation of the André-Oort and André-Pink-Zannier Conjectures
Rodolphe Richard, Andrei Yafaev
We introduce a ``hybrid'' conjecture which is a common generalisation of the André-Oort conjecture and the André-Pink-Zannier conjecture and we prove that it is a consequence of th…
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…
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…
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…
Constructing abelian extensions with prescribed norms
Christopher Frei, Rodolphe Richard
Given a number field , a finite abelian group and finitely many elements , we construct abelian extensions with Galois group that realise all…
Homogeneous Dynamics and Unlikely Intersections
R. Richard, A. Yafaev, T. Zamojski
This is a preliminary version of a monograph on homogeneous dynamics and application to some problems of unlikely intersections in Shimura varieties. It consists of four articles,…
A two dimensional arithmetic André-Oort problem
Rodolphe Richard
We state and investigate an integral analogue of the André-Oort conjecture (in integral models of Shimura varieties). We establish an instance of this conjecture: the case of a mod…
A mod p variant of the André-Oort conjecture
Bas Edixhoven, Rodolphe Richard
We state and prove a variant of the André-Oort conjecture for the product of 2 modular curves in positive characteristic, assuming GRH for quadratic fields.
Inner Galois Equidistribution in S-Hecke orbits
Rodolphe Richard, Andrei Yafaev
We obtain results on the so-called Andre-Pink-Zannier conjecture which is a special case of a the Zilber-Pink conjecture on unlikely intersections in Shimura varieties. Our methods…
Limit distribution of Translated pieces of possibly irrational leaves in S-arithmetic homogeneous spaces
Rodolphe Richard, Thomas Zamojski
The purpose of this article is to describe and characterize the limit distributions of translates of a bounded open "piece of orbit" of a reductive subgroup on a space of S-arithme…
On π-exponentials II : Closed formula for the index
Rodolphe Richard
(Quoted from the article) This article pursue the series, initiated by [Ric14], dedicated to Pulita's π-exponentials and p-adic differential equation of rank one with coefficients…
Geometric results on linear actions of reductive Lie groups for applications to homogeneous dynamics
Rodolphe Richard, Nimish A. Shah
Several problems in number theory when reformulated in terms of homogenous dynamics involve study of limiting distributions of translates of algebraically defined measures on orbit…