Algebra Seminar

On the Shafarevich-Tate and Selmer groups of an elliptic curve over the field of rational numbers.
Monday, 27 February 2017 - 1:10 pm to 1:40 pm
Location
Room number: 
HP 4325 (Carleton)
Registration
Registration required: 
No
Cost to attend: 
Free of charge
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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.