Arithmetic Veech sublattices of SL(2,Z)

Abstract

We prove that every algebraic curve $X/\overline{\mathbf{Q}}$ is birational over $\mathbf{C}$ to a Teichmüller curve. This result is a corollary of our main theorem, which asserts that most finite-index subgroups of $SL(2,\mathbf{Z})$ are Veech groups.