English

Categoricity of the two sorted j-function

Logic 2013-04-18 v1

Abstract

We show that a natural, two sorted \cLω1,ω\cL_{\omega_1,\omega} theory involving the modular jj-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.

Keywords

Cite

@article{arxiv.1304.4787,
  title  = {Categoricity of the two sorted j-function},
  author = {Adam Harris},
  journal= {arXiv preprint arXiv:1304.4787},
  year   = {2013}
}
R2 v1 2026-06-22T00:01:33.839Z