Friday, March 2, 2018
Building 15, Room 122
Number Theory Seminar
Singular moduli for real quadratic fields
Jan Vonk, Department of Mathematics and Statistics, McGill University
The theory of complex multiplication describes finite abelian extensions of imaginary quadratic number fields using singular moduli, which are special values of modular functions at CM points. Hilbert's 12th problem asks for a satisfactory analogue of this theory for arbitrary number fields. I will describe joint work with Henri Darmon in the setting of real quadratic fields, where we construct p-adic analogues of singular moduli through classes of rigid meromorphic cocycles.