Selmer classes on CM elliptic curves of rank 2

Abstract: Let E be an elliptic curve over Q, and let p be a prime of good ordinary reduction for E. Following the pioneering 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 order. In this talk, I'll report on the proof of an analogue of Skinner's result in the rank 2 case, in which Heegner points are replaced by certain generalized Kato classes introduced by Darmon-Rotger. For E without CM, such an analogue was obtained in an earlier work with M.-L. Hsieh, and in this talk I'll focus on the CM case, whose proof uses a different set of ideas.

number theory

Audience: researchers in the topic

( slides )

UCLA Number Theory Seminar