Congruences of modular forms and Tate—Shafarevich classes

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• Matteo Tamiozzo
• Tuesday 06 June 2023, 14:30-15:30
• MR2.

If you have a question about this talk, please contact Rong Zhou.

I will present two applications of level raising of modular forms to the study of the Tate—Shafarevich group of modular elliptic curves over totally real fields. Firstly, I will explain how to bound above the size of the p-part of the Tate—Shafarevich group of elliptic curves of analytic rank at most one. Secondly, I will discuss how to construct visible Tate—Shafarevich classes, as predicted by a conjecture of Jetchev—Stein.

This talk is part of the Number Theory Seminar series.

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