Plectic Stark-Heegner points
Plectic Stark-Heegner points
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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.