International Seminar on Automorphic Forms

Hazem Hassan (McGill)

Heegner Cycles are higher weight generalizations of Heegner points on Modular curves. As such, one expects them to capture similar arithmetic and modular properties to Heegner points. The higher dimensional nature of Heegner cycles makes them less amenable to algebro-geometric and deformation theoretic approaches. I will introduce Stark-Heegner Cycles, which are a conjectural analogue to Heegner Cycles in the theory of Real Multiplication. They are defined through p-adic analytic means. Then, I will describe a p-adic pairing on these cycles which behaves as a local height pairing. When one of the cycles is principal, the pairing computationally seems to produce algebraic integers living in class fields of real quadratic fields.

https://tu-darmstadt.zoom.us/j/68048280736

The password is the first Fourier coefficient of the modular j-function (as digits)