Shimura curves in the Prym locus

Prym varieties and Teichmüller curves

This paper gives a uniform construction of infinitely many primitive Teichmüller curves V ⊂ Mg for g = 2, 3 and 4.

Notes on Shimura curves

Unitary Cycles on Shimura Curves and the Shimura Lift I

This paper concerns two families of divisors, which we call the ‘orthogonal’ and ‘unitary’ special cycles, defined on integral models of Shimura curves. The orthogonal family was studied extensively by Kudla-Rapoport-Yang, who showed that they are closely related to the Fourier coefficients of modular forms of weight 3/2, while the unitary divisors are analogues of cycles appearing in more rece...

Lectures on Shimura Curves 0: Modular Curves

General remarks about these documents: These are lecture notes. Let us reflect separately on the meaning of both words. The first word is meant to indicate some correspondence between what is said in the lectures and what appears in these notes. This correspondence is not precise: on the one hand, in response to a question or a comment, I may say things in class which do not make it into these ...

Singular Moduli of Shimura Curves

The j-function acts as a parametrization of the classical modular curve. Its values at complex multiplication (CM) points are called singular moduli and are algebraic integers. A Shimura curve is a generalization of the modular curve and, if the Shimura curve has genus 0, a rational parameterizing function exists and when evaluated at a CM point is again algebraic over Q. This paper shows that ...