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pro vyhledávání: '"RICHARD, Rodolphe"'
Autor:
Richard, Rodolphe, Yafaev, Andrei
We prove the 'hybrid conjecture' which is a common generalisation of the Andre\'e-Oort conjecture and the Andr\'e-Pink-Zannier conjecture, in the case of Shimura varieties of abelian type.
Externí odkaz:
http://arxiv.org/abs/2406.20013
Autor:
Richard, Rodolphe, Yafaev, Andrei
We introduce a ``hybrid'' conjecture which is a common generalisation of the Andr\'e-Oort conjecture and the Andr\'e-Pink-Zannier conjecture and we prove that it is a consequence of the Zilber-Pink conjecture. We also show that our hybrid conjecture
Externí odkaz:
http://arxiv.org/abs/2401.03528
Autor:
Richard, Rodolphe, Yafaev, Andrei
In this paper, we prove the generalised Andr\'e-Pink-Zannier conjecture (an important case of the Zilber-Pink conjecture) for all Shimura varieties of abelian type. Questions of this type were first asked by Y. Andr\'e in 1989. We actually prove a ge
Externí odkaz:
http://arxiv.org/abs/2111.11216
Autor:
Richard, Rodolphe, Yafaev, Andrei
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
Externí odkaz:
http://arxiv.org/abs/2109.13718
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 modulo some, possibly varying, prime of Galois orbits of torsion points. T
Externí odkaz:
http://arxiv.org/abs/2105.12027
A characterization of subvarieties of Shimura varieties which contain a Zariski dense subset of weakly special subvarieties has been proved by the second author, by combining o-minimality results and functional transcendence results. In this paper, w
Externí odkaz:
http://arxiv.org/abs/2104.04439
Autor:
Frei, Christopher, Richard, Rodolphe
Given a number field $K$, a finite abelian group $G$ and finitely many elements $\alpha_1,\ldots,\alpha_t\in K$, we construct abelian extensions $L/K$ with Galois group $G$ that realise all of the elements $\alpha_1,\ldots,\alpha_t$ as norms of eleme
Externí odkaz:
http://arxiv.org/abs/2006.08968
Akademický článek
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Autor:
Richard, Rodolphe
We state and investigate an integral analogue of the Andr\'e-Oort conjecture (in integral models of Shimura varieties). We establish an instance of this conjecture: the case of a modular curve, as a scheme over Z. It is a scheme of dimension two and,
Externí odkaz:
http://arxiv.org/abs/1808.07900
Autor:
Edixhoven, Bas, Richard, Rodolphe
We state and prove a variant of the Andr\'e-Oort conjecture for the product of 2 modular curves in positive characteristic, assuming GRH for quadratic fields.
Externí odkaz:
http://arxiv.org/abs/1807.03607