Elliptic curves of rank 2 and generalised Kato classes

02.03.2021 15:15 - 16:45

Francesc Castella (UC Santa Barbara)

Let E be a rational elliptic curve with global root number +1, and let p be a prime of good ordinary reduction for E. By p-adically deforming diagonal cycles on triple products of modular curves (and Kuga-Sato varieties over them), a construction of Darmon-Rotger associates to E a global cohomology class that is known to be crystalline at p precisely when L(E,s) vanishes at s=1. In this talk, I will explain the proof (under some hypotheses) that this class is nonzero precisely when the p-adic Selmer group of E is 2-dimensional, as was conjectured by Darmon and Rotger. This is joint work with Ming-Lun Hsieh.

Note the unusual time!


H. Grobner, A. Minguez-Espallargas, A. Mellit

Meeting ID: 431 655 310, Passcode: 0cnL5d