Speaker: Karl Rubin
Title: Selmer modules and skew-Hermitian matrices
Abstract: Suppose $E$ is an elliptic curve defined over a number field $K$, and $p$ is a prime where $E$ has good ordinary reduction. We wish to study the Selmer groups of $E$ over all finite extensions $L$ of $K$ contained in the maximal ${\bf Z}_p$-power extension of $K$, along with their $p$-adic height pairings and a Cassels pairings. Our goal is to produce a single free Iwasawa module of finite rank, with a skew-Hermitian pairing, from which we can recover all of this data. Using recent work of Nekovar we can show that (under mild hypotheses) such an `organizing module' exists, and we will give some examples. This work is joint with Barry Mazur.