SPEAKER: Francois Destrempes (N/A) DATE: Monday, February 27, 2017 TIME: 1:10 pm ROOM: HP 4325 (Carleton) ABSTRACT:
The Shafarevich-Tate and Selmer groups arise in the context of Kummer theory for elliptic curves. The finiteness of the Shafarevich-Tate group of an elliptic curve E over the field of rational numbers is included in the Birch and Swinnerton-Dyer conjectures, and is still an open question.
We will present an overview of the Shafarevich-Tate and Selmer groups of an elliptic curve in the framework of group cohomology. Known results on the finiteness of the Shafarevich-Tate group will be mentioned, including results of Rubin and Kolyvagin.
We will then discuss the vanishing of the p-component of the torsion subgroup of the Shafarevich-Tate group for almost all primes p, under the assumption that the elliptic curve E has non-integral j-invariant. This is original joint work of the speaker with Dmitry Malinin.