Hemming Ma: Moduli of elliptic curves with isogenies

Abstract: A moduli problem involves classifying geometric objects as points of a space. For some objects, such as elliptic curves, non-trivial automorphisms prevent this space from being a scheme. The solution is to use a generalization of schemes called algebraic stacks, which incorporate automorphisms as part of the data. It is classical that there exists an algebraic stack parameterizing elliptic curves. In this thesis, we consider an extension of this stack where the objects now consist of an elliptic curve along with an automorphism and show that it is also algebraic.