Algebraicity of polyquadratic plectic points

Abstract: Heegner points play an important role in our understanding of the arithmetic of modular elliptic curves. These points, that arise from CM points on Shimura curves, control the Mordell-Weil group of elliptic curves of rank 1. The work of Bertolini, Darmon and their schools has shown that p-adic methods can be successfully employed to generalize the definition of Heegner points to quadratic extensions that are not necessarily CM. Numerical evidence strongly supports the belief that these so-called Stark-Heegner points completely control the Mordell-Weil group of elliptic curves of rank 1. In this talk I will report on a plectic generalizations of Stark-Heegner points. Inspired by Nekovar and Scholl's conjectures, these points are expected to control Mordell-Weil groups of higher rank elliptic curves. I will give strong evidence for this expectation in the case of polyquadratic CM fields. This is joint work with Michele Fornea.

algebraic geometrynumber theory

Audience: researchers in the topic

Number Theory Seminars at Università degli Studi di Padova