Categoricity of the two sorted j-function

2013/04/17 by Adam Harris, Harris, Adam · 1 citation
Mathematics · Engineering · #Advanced Statistical Methods and Models #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1304.4787

Abstract

We show that a natural, two sorted \cL_ω1,ω theory involving the modular j-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.

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