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!