Expander graphs, gonality and variation of Galois representations

Details Expander graphs, gonality and variation of Galois representations Expander graphs, gonality and variation of Galois representations

2010-08-22

arxiv.org/abs/1008.3675v4

Mathematics

Number Theory

32 pages; v4: changes mostly in exposition

Scientific paper

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.

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