## Speaker:

Professor Karl Rubin

## Institution:

UCI

## Time:

Tuesday, November 16, 2004 - 3:00pm

## Location:

MSTB 256

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 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.