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SUMMARY:Yukako Kezuka (Jussieu)
DTSTART:20220629T150000Z
DTEND:20220629T160000Z
DTSTAMP:20260418T064328Z
UID:LNTS/75
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/75/">Ar
 ithmetic of elliptic curves with complex multiplication at small primes</a
 >\nby Yukako Kezuka (Jussieu) as part of London number theory seminar\n\nL
 ecture held in King's Building K0.18.\n\nAbstract\nThe equation E: x^3+y^3
 =N defines a classical family of elliptic curves as N varies over cube-fre
 e positive integers. They admit complex multiplication\, which allows us t
 o tackle the conjecture of Birch and Swinnerton-Dyer for E effectively. In
 deed\, using Iwasawa theory\, Rubin was able to show the p-part of the con
 jecture for E for all primes p\, except for the primes 2 and 3. The theory
  becomes much more complex at these small primes\, but at the same time we
  can observe some interesting phenomena. I will explain a method to study 
 the p-adic valuation of the algebraic part of the central L-value of E\, a
 nd I will establish the 3-part of the conjecture for E in special cases. I
  will then explain a relation between the 2-part of a certain ideal class 
 group and the Tate-Shafarevich group of E. Part of this talk is based on j
 oint work with Yongxiong Li.\n
LOCATION:https://researchseminars.org/talk/LNTS/75/
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