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SUMMARY:Naomi Sweeting (Harvard)
DTSTART:20210426T230000Z
DTEND:20210426T235000Z
DTSTAMP:20260423T022921Z
UID:UCLA_NTS/29
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCLA_NTS/29/
 ">Kolyvagin's conjecture and higher congruences of modular forms</a>\nby N
 aomi Sweeting (Harvard) as part of UCLA Number Theory Seminar\n\n\nAbstrac
 t\nGiven an elliptic curve $E$\,  Kolyvagin used CM points on modular curv
 es to construct a system of classes valued in the Galois cohomology of the
  torsion points of $E$. Under the conjecture that not all of these classes
  vanish\, he gave a description for the Selmer group of $E$.  This talk wi
 ll report on recent work proving new cases of Kolyvagin's conjecture. The 
 proof builds on work of Wei Zhang\, who used congruences between modular f
 orms to prove Kolyvagin's conjecture under some technical hypotheses. We r
 emove many of these hypotheses by considering congruences modulo higher po
 wers of $p$. The talk will explain the difficulties associated with higher
  congruences of modular forms and how they can be overcome\n
LOCATION:https://researchseminars.org/talk/UCLA_NTS/29/
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