BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Francesc Castella (UCSB)
DTSTART:20201027T210000Z
DTEND:20201027T220000Z
DTSTAMP:20260423T041505Z
UID:UAANTS/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UAANTS/4/">I
 wasawa theory of elliptic curves at Eisenstein primes and applications</a>
 \nby Francesc Castella (UCSB) as part of University of Arizona Algebra and
  Number Theory Seminar\n\n\nAbstract\nIn the study of Iwasawa theory of el
 liptic curves $E/\\mathbb{Q}$\, it is often assumed that $p$ is a non-Eise
 nstein prime\, meaning that $E[p]$ is irreducible as a $G_{\\mathbb{Q}}$-m
 odule. Because of this\, most of the recent results on the $p$-converse to
  the theorem of Gross–Zagier and Kolyvagin (following Skinner and Wei Zh
 ang) and on the $p$-part of the Birch–Swinnerton-Dyer formula in analyti
 c rank 1 (following Jetchev–Skinner–Wan) were only known for non-Eisen
 stein 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 ove
 r $\\mathbb{Q}$ at Eisenstein primes. As a consequence of our study\, we o
 btain an extension of the aforementioned results to the Eisenstein case. I
 n particular\, for $p=3$ this leads to an improvement on the best known re
 sults towards Goldfeld’s conjecture in the case of elliptic curves over 
 $\\mathbb{Q}$ with a rational $3$-isogeny.\n
LOCATION:https://researchseminars.org/talk/UAANTS/4/
END:VEVENT
END:VCALENDAR