The University of Sydney
School of Mathematics and Statistics  
Number Theory Seminar  

University of Sydney Number Theory Seminar

John Voight

Friday 7 April 2006, 1:05-2:00PM, Carslaw 251

Shimura curves as moduli spaces

Over the complex numbers, a Shimura curve is a Riemann surface which is uniformized by an arithmetic Fuchsian group. Such curves in fact have a much richer structure: they are (coarse) moduli spaces for certain abelian varieties with extra endomorphisms. In this discussion, we present an account of this theory which will focus on two cases of particular interest: curves over the rational numbers and curves uniformized by arithmetic triangle groups.