Plectic Stark-Heegner points
Plectic Stark-Heegner points
-
Michele Fornea, Columbia University
In-Person and Online Talk
Meeting ID:Ìý 920 2195 5230
Passcode:Ìý Ìý The three-digit integer that is the cube of the sum of its digits.Ìý
I will report on a series of joint works with Gehrmann, Guitart and Masdeu about aÌýplectic generalization of Darmon's Stark-Heegner (SH) points.ÌýWe constructed plectic SH points as p-adic points on elliptic curves and we expect them to control theÌýarithmetic of higher rank Mordell-Weil groups. To support our conjecturesÌýwe numerically verified them in many cases, weÌýestablished an explicit relation between plectic SH points and higher derivatives ofÌý?-²¹»å¾±³¦Ìý?-functions, and we proved the algebraicity of plectic points in special cases.
Ìý