A model theory of modular curves
I am going to discuss a progress in a project which aims to formalise the notion of an analytic covering space of a complex algebraic variety
in such a way that the formal pseudo-analytic cover is unique up to abstract isomorphisms. At this stage our interest focuses on the upper half-plane as the cover of modular curves.
On the model theory side it is based on Shelah's theory of abstract elementary classes. On the geometric side it uses the rich theory of complex multiplication and
canonical models of Shimura varieties as developed by Shimura, Langlands, Deligne, Milne, Borovoi and others.
תאריך עדכון אחרון : 04/05/2021