A two dimensional arithmetic Andr\'e-Oort problem
Number Theory
2021-12-21 v2
Abstract
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, already in this case, our conjecture is highly non-trivial. Our approach relies on equidistribution estimates related to subconvexity in analytic number theory and our result is unconditional.
Cite
@article{arxiv.1808.07900,
title = {A two dimensional arithmetic Andr\'e-Oort problem},
author = {Rodolphe Richard},
journal= {arXiv preprint arXiv:1808.07900},
year = {2021}
}