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15 May 2012 Expander graphs, gonality, and variation of Galois representations
Jordan S. Ellenberg, Chris Hall, Emmanuel Kowalski
Duke Math. J. 161(7): 1233-1275 (15 May 2012). DOI: 10.1215/00127094-1593272

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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Jordan S. Ellenberg. Chris Hall. Emmanuel Kowalski. "Expander graphs, gonality, and variation of Galois representations." Duke Math. J. 161 (7) 1233 - 1275, 15 May 2012. https://doi.org/10.1215/00127094-1593272

Information

Published: 15 May 2012
First available in Project Euclid: 4 May 2012

zbMATH: 1262.14021
MathSciNet: MR2922374
Digital Object Identifier: 10.1215/00127094-1593272

Subjects:
Primary: 05C40 , 05C50 , 14D10 , 14G05
Secondary: 14D05 , 14K15 , 35P15

Rights: Copyright © 2012 Duke University Press

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Vol.161 • No. 7 • 15 May 2012
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