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SUMMARY:Francesc Castella (UC Santa Barbara)
DTSTART:20201020T203000Z
DTEND:20201020T213000Z
DTSTAMP:20260423T130123Z
UID:MITNT/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITNT/11/">I
 wasawa theory of elliptic curves at Eisenstein primes and applications</a>
 \nby Francesc Castella (UC Santa Barbara) as part of MIT number theory sem
 inar\n\n\nAbstract\nIn the study of Iwasawa theory of elliptic curves $E/\
 \mathbb{Q}$\, it is often assumed that $p$ is a non-Eisenstein prime\, mea
 ning that $E[p]$ is irreducible as a $G_{\\mathbb{Q}}$-module. Because of 
 this\, most of the recent results on the $p$-converse to the theorem of Gr
 oss–Zagier and Kolyvagin (following Skinner and Wei Zhang) and on the $p
 $-part of the Birch–Swinnerton-Dyer formula in analytic rank 1 (followin
 g 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 th
 e (anticyclotomic) Iwasawa theory of elliptic curves over $\\mathbb{Q}$ 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 Gold
 feld’s conjecture in the case of elliptic curves over $\\mathbb{Q}$ with
  a rational $3$-isogeny.\n
LOCATION:https://researchseminars.org/talk/MITNT/11/
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