Rigid meromorphic cocycles and p-adic variations of modular forms

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• Alice Pozzi, Imperial College London
• Tuesday 15 March 2022, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Rong Zhou.

A rigid meromorphic cocycle is a class in the first cohomology of the group SL2 acting on the non-zero rigid meromorphic functions on the Drinfeld p-adic upper half plane by M¨obius transformation. Rigid meromorphic cocycles can be evaluated at points of “real multiplication”, and their values conjecturally lie in composita of abelian extensions of real quadratic fields, suggesting striking analogies with the classical theory of complex multiplication. In this talk, we discuss the proof of this conjecture for a special class of rigid meromorphic cocycles. Our proof connects the values of rigid meromorphic cocycles to the study of certain p-adic variations of Hilbert modular forms. This is joint work with Henri Darmon and Jan Vonk.

This talk is part of the Number Theory Seminar series.

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