Journal of Differential Geometry

Finding large Selmer Groups

Barry Mazur and Karl Rubin

Abstract

In this paper, we show how to use a recent theorem of Nekovář [12] to produce families of examples of elliptic curves over number fields whose p-power Selmer groups grow systematically in Zpd-extensions. We give a somewhat different exposition and proof of Nekovář's theorem, and we show in many cases how to replace the fundamental requirement that the elliptic curve has odd p-Selmer rank by a root number calculation.

Article information

Source
J. Differential Geom. Volume 70, Number 1 (2005), 1-22.

Dates
First available in Project Euclid: 28 March 2006

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1143572012

Digital Object Identifier
doi:10.4310/jdg/1143572012

Mathematical Reviews number (MathSciNet)
MR2192059

Zentralblatt MATH identifier
1211.11068

Citation

Mazur, Barry; Rubin, Karl. Finding large Selmer Groups. J. Differential Geom. 70 (2005), no. 1, 1--22. doi:10.4310/jdg/1143572012. https://projecteuclid.org/euclid.jdg/1143572012.


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