Finding large Selmer Groups

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 Z_p^d-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.