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.