##### Department of Mathematics,

University of California San Diego

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### Special Colloquium

## Jonathan Pottharst

#### Boston University

## Iwasawa theory of supersingular elliptic curves

##### 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 Birchâ€“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.

Host: Kiran Kedlaya

### January 8, 2013

### 3:00 PM

### AP&M 6402

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