Joint IAS/PU Number Theory Seminar

I will report on a series of joint works with Gehrmann, Guitart and Masdeu about a plectic generalization of Darmon's Stark-Heegner (SH) points. 

We constructed plectic SH points as p-adic points on elliptic curves and we expect them to control the arithmetic of higher rank Mordell-Weil groups. To support our conjectures we numerically verified them in many cases, we established an explicit relation between plectic SH points and higher derivatives of 𝑝-adic 𝐿-functions, and we proved the algebraicity of plectic points in special cases.