# W. Stein: Shafarevich-Tate Groups of Elliptic Curves of Rank at Least Two

## May 20, 2011 in Padelford C401 at 3:30pm

## Abstract

Consider the set X of pairs (E,p), where E is an elliptic curve of rank at least 2 and p is a prime such that the p-primary part of the Shafarevich-Tate group of E is finite. It is an open problem to prove that X is infinite! I will talk about various approaches to this extremely difficult unsolved problem.

## Notes

I typed up notes for a related talk, though my talk today will be somewhat different.