Gamma(n) structures

I gave this talk on the 27th of October of 2023 for the study group on moduli problems of elliptic curves organised by Elvira Lupoian.

The goal of the study group was to understand the foundations of the arithmetic theory of moduli spaces of elliptic curves. In my talk, I explained the theory of Cartier divisors and how they can be used to define \(\Gamma(n), \Gamma_1(n)\) and \(\Gamma_0(n)\)-structures on elliptic curves defined over a scheme. These are the notes I wrote for my talk: