Plectic Stark-Heegner points

Michele Fornea, Columbia University
Fine Hall 214

In-Person and Online Talk

Meeting ID:  920 2195 5230

Passcode:    The three-digit integer that is the cube of the sum of its digits. 

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 ?-adic ?-functions, and we proved the algebraicity of plectic points in special cases.