QM abelian surfaces

Abstract

In this final chapter, we consider quotients of the upper half-plane by quaternionic unit groups as generalizations of such quotients from the matrix group (Chapter 40), realizing them as moduli spaces for abelian surfaces with quaternionic multiplication. This chapter can be seen as a culminating application of all of the parts of this book, and for that reason, is necessarily more advanced. Concepts are reviewed in the attempt to be self-contained, but additional background in algebraic and arithmetic geometry is suggested.