Modular curves and their deep connections with arithmetic have been a central focus of research for the past century. But their geometric structure, both over the complex numbers and integrally over Z, or over finite fields, is deceptively simple and provides little idea of the intricacies that arise for Shimura varieties of higher dimension. The Shimura varieties attached to unitary groups for imaginary quadratic fields K provide a particularly attractive next case.

Registration is free but mandatory