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SUMMARY:Congruences of modular forms and Tate—Shafarevich classes - Matt
 eo Tamiozzo
DTSTART:20230606T133000Z
DTEND:20230606T143000Z
UID:TALK200374@talks.cam.ac.uk
CONTACT:Rong Zhou
DESCRIPTION:I will present two applications of level raising of modular fo
 rms to the study of the Tate—Shafarevich group of modular elliptic curve
 s over totally real fields. Firstly\, I will explain how to bound above th
 e 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 vis
 ible Tate—Shafarevich classes\, as predicted by a conjecture of Jetchev
 —Stein.
LOCATION:MR2
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