Expander Graphs, Gonality and Variation of Galois Representations
نویسندگان
چکیده
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 growth. Combining this general result with finiteness statements for rational points under such conditions, we derive results concerning the variation of Galois representations in oneparameter families of abelian varieties.
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