Categoricity and covering spaces
Adam Harris

TL;DR
This thesis explores the model theory of algebraic curve covers, linking the behavior of the modular j-function with properties of Galois representations in Tate-modules of abelian varieties.
Contribution
It establishes an equivalence between model-theoretic properties of covers and the openness of Galois representations, connecting algebraic geometry and model theory.
Findings
Equivalence between model-theoretic behavior and Galois representation openness
Insights into the structure of covers of algebraic curves
Connections between the modular j-function and Galois actions
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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Polynomial and algebraic computation
