[Quadranscentennial KIAS Lecture] Prof. Henri Darmon II

[Quadranscentennial KIAS Lecture] The theory of complex multiplication, and beyond II
Professor Henri Darmon (McGill University)
September 2, 2021

The theory of complex multiplication gives an explicit construction of abelian extensions of quadratic imaginary fields (or more general CM fields) from the values of modular functions on modular curves (or more general higher dimensional Shimura varieties) at CM points. We will describe an approach to extending this theory beyond the setting of CM fields, in which modular functions are replaced by ``rigid meromorphic cocycles”.