Points on elliptic curves via p-adic integration

Abstract: The work of Bertolini, Darmon and their schools has shown that p-adic multiplicative integrals can be successfully employed to study the global arithmetic of elliptic curves. Notably, Guitart, Masdeu and Sengun have recently constructed and numerically computed Stark-Heegner points in great generality. Their results strongly support the expectation that Stark-Heegner points completely control the Mordell-Weil group of elliptic curves of rank 1.

In our talk, we will report on work in progress about a conjectural construction of global points on modular elliptic curves, generalizing the p-adic construction of Heegner points via Cerednik-Drinfeld uniformization. Inspired by Nekovar and Scholl's plectic conjectures, we expect the non-triviality of these plectic Heegner points to control the Morderll-Weil group of higher rank elliptic curves. We provide some evidence for our conjectures by showing that higher derivatives of anticyclotomic p-adic L-functions compute plectic Heegner points.

number theory

Audience: researchers in the topic

Columbia Automorphic Forms and Arithmetic Seminar