Selmer groups and skew-Hermitian matrices

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.

On the function field height zeta function

Speaker: 

Mr. Doug. Haessig

Institution: 

UC Irvine

Time: 

Tuesday, October 19, 2004 - 3:00pm

Location: 

MSTB 256

Let X be a projective variety over a finite field
with function field K(X). Let Y be a projective variety
over K(X). We may associate to this a height zeta
function. In this talk, we will recall some facts
about these functions and provide some new results
and research directions.

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