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Featured Speaker:  Francesca Castella (University of California, Santa Barbara)

Title:  Iwasawa theory of elliptic curves at Eisenstein primes and applications 

Abstract: In the study of Iwasawa theory of elliptic curves p a non-Eisenstein prime, meaning that E[p] is irreducible as a G-module. Because of this, most of the recent results on the p-converse to the theorem of Gross–Zagier and Kolyvagin (following Skinner and Wei Zhang) and on the p-part of the Birch–Swinnerton-Dyer formula in analytic rank 1 (following Jetchev–Skinner–Wan) were only known for non-Eisenstein primes p. In this talk, I’ll explain some of the ingredients in a joint work with Giada Grossi, Jaehoon Lee, and Christopher Skinner in which we study the (anticyclotomic) Iwasawa theory of elliptic curves over ℚ at Eisenstein primes. As a consequence of our study, we obtain an extension of the aforementioned results to the Eisenstein case. In particular, for p = 3 this leads to an improvement on the best known results towards Goldfeld’s conjecture in the case of elliptic curves over ℚ with a rational 3-isogeny.

 

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