Selmer groups and Mordell–Weil groups of elliptic curves over towers of function fields

Jordan S. Ellenberg

Type: Article

Publication Date: 2006-09-01

Citations: 16

DOI: https://doi.org/10.1112/s0010437x0600217x

Abstract

Silverman has discussed the problem of bounding the Mordell–Weil ranks of elliptic curves over towers of function fields (J. Algebraic Geom. 9 (2000), 301–308; J. reine. angew. Math. 577 (2004), 153–169). We first prove generalizations of the theorems of Silverman by a different method, allowing non-abelian Galois groups and removing the dependence on Tate's conjectures. We then prove some theorems about the growth of Mordell–Weil ranks in towers of function fields whose Galois groups are , and show that these criteria are met for elliptic K3 surfaces whose associated Galois representations have sufficiently large image.

Locations

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