Submission date: 10 December 2014

Abstract:

This thesis develops some of the basic model theory of covers of algebraic curves. In particular, an equivalence between the good model-theoretic behaviour of the modular j-function, and the openness of certain Galois representations in the Tate-modules of abelian varieties is described.

Mathematics Subject Classification: 11G18 (Primary), 03C35 (Secondary)

Keywords and phrases:

Full text arXiv 1412.3484: pdf, ps.