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The values of the Dedekind-Rademacher cocycle at real multiplication points

Leertaste = Abspielen/Pausieren
m = Stumm
f = Vollbild
Pfeil-links = Zurückspulen
Pfeil-rechts = Vorspulen
Alice Pozzi

The values of the Dedekind-Rademacher cocycle at real multiplication points

A rigid meromorphic cocycle is a class in the first cohomology of the group SL2(Z[1/p]) acting on the non-zero rigid meromorphic functions on the Drinfeld p-adic upper half plane by Möbius transformation. Rigid meromorphic cocycles can be evaluated at points of real multiplication, and their RM values conjecturally lie in the ring class field of real quadratic fields, suggesting a striking analogy with the classical theory of complex multiplication. In this talk, we discuss a special case of the conjecture, relating the RM values of the "Eisenstein" Dedekind-Rademacher cocycle to a Gross-Stark unit. We explain the construction of this cocycle, and the connection between the algebraicity of its RM values and certain deformations of Hilbert Eisenstein series of weight one. This is joint work with Henri Darmon and Jan Vonk.