Jonathan Pottharst : Iwasawa theory of supersingular elliptic curves

Posted by Ramin Takloo-Bighash , part of the Number Theory Seminar.

At

Nov. 15, 2012, 3 p.m.

In

SEO 636

Abstract

Given an elliptic curve $E/{\mathbb Q}$ with good reduction at p, Iwasawa theory studies its arithmetic over all the fields of $p^n$-th roots of unity. For example, there are nontrivial relations among the participants in the Birch–Swinnerton-Dyer conjectures for $E$ over each layer in this tower of fields. If the reduction of $E \mod p$ is ordinary, then have had a satisfactory description of the scenario for quite some time. But if the reduction of $E \mod p$ is supersingular, the correct description has required new advances in $p$-adic Hodge theory. We will discuss the background and what is now known, and then, time permitting, describe the new tools and how they fit into an emerging larger picture of $p$-adic number theory.

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