Derivatives of Hida families, diagonal restriction and rigid meromorphic cocycles

Abstract: A rigid meromorphic cocycle is a class in the first cohomology of the group $\SL_2(\mathbf Z[1/p])$ acting on the non-zero rigid meromorphic functions on the Drinfeld p-adic upper half plane by Möbius transformation. The values of rigid meromorphic cocycles at real quadratic points are conjecturally algebraic and are expected to play a role in the explicit class field theory for real quadratic fields.

In this talk, we discuss the connection between values of rigid meromorphic cocycles at real multiplication points and derivatives of Hida families for real quadratic fields. We explain how this relation can be exploited to deduce the algebraicity of real multiplication values in some cases. This is joint work with Henri Darmon and Jan Vonk.

algebraic geometrynumber theory

Audience: researchers in the topic

Séminaire de géométrie arithmétique et motivique (Paris Nord)