Categoricity of the two sorted j-function
Logic
2013-04-18 v1
Abstract
We show that a natural, two sorted theory involving the modular -function is categorical in all uncountable cardinaities. It is also shown that a slight weakening of the adelic Mumford-Tate conjecture for products of elliptic curves is necessary and (along with a couple of other results from arithmetic geometry) sufficient for categoricity.
Cite
@article{arxiv.1304.4787,
title = {Categoricity of the two sorted j-function},
author = {Adam Harris},
journal= {arXiv preprint arXiv:1304.4787},
year = {2013}
}