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SUMMARY:Francesc Castella (UC Santa Barbara)
DTSTART:20220131T230000Z
DTEND:20220131T235000Z
DTSTAMP:20260423T041508Z
UID:UCLA_NTS/44
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCLA_NTS/44/
 ">Selmer classes on CM elliptic curves of rank 2</a>\nby Francesc Castella
  (UC Santa Barbara) as part of UCLA Number Theory Seminar\n\nLecture held 
 in Math Science 5118.\n\nAbstract\nLet E be an elliptic curve over Q\, and
  let p be a prime of good ordinary reduction for E. Following the pioneeri
 ng work of Skinner (and independently Wei Zhang) from about 8 years ago\, 
 there is a growing number of results in the direction of a p-converse to a
  theorem of Gross-Zagier and Kolyvagin\, showing that if the p-adic Selmer
  group of E is 1-dimensional\, then a Heegner point on E has infinite orde
 r. In this talk\, I'll report on the proof of an analogue of Skinner's res
 ult in the rank 2 case\, in which Heegner points are replaced by certain g
 eneralized Kato classes introduced by Darmon-Rotger. For E without CM\, su
 ch an analogue was obtained in an earlier work with M.-L. Hsieh\, and in t
 his talk I'll focus on the CM case\, whose proof uses a different set of i
 deas.\n
LOCATION:https://researchseminars.org/talk/UCLA_NTS/44/
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