vix.ing · top · new · best · stats · spec

A two dimensional arithmetic André-Oort problem

2018/08/23 by Richard, Rodolphe · 1 citation
#11E12 #11F11 #11F23 #11G15 #11G18 #14G35 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1808.07900

Abstract

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 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.

Cited by

Related