Expander graphs, gonality and variation of Galois representations
Number Theory
2019-12-19 v4
Abstract
We show that families of coverings of an algebraic curve where the associated Cayley-Schreier graphs form an expander family exhibit strong forms of geometric (genus and gonality) growth. Combining this general result with finiteness statements for rational points under such conditions, we derive results concerning the variation of Galois representations in one-parameter families of abelian varieties.
Keywords
Cite
@article{arxiv.1008.3675,
title = {Expander graphs, gonality and variation of Galois representations},
author = {Jordan Ellenberg and Chris Hall and Emmanuel Kowalski},
journal= {arXiv preprint arXiv:1008.3675},
year = {2019}
}
Comments
32 pages; v4: changes mostly in exposition