Expander graphs, gonality, and variation of Galois representations
Jordan S. Ellenberg, Chris Hall, and Emmanuel Kowalski
Source: Duke Math. J. Volume 161, Number 7
(2012), 1233-1275.
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 growth. We then give many arithmetic applications of this general result, obtained by combining it with finiteness statements for rational points of curves with large gonality. In particular, we derive a number of results concerning the variation of Galois representations in one-parameter families of abelian varieties.
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1336142075
Digital Object Identifier: doi:10.1215/00127094-1593272
Zentralblatt MATH identifier: 06047810
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