Resumen de Differential equations associated with nonarithmetic Fuchsian groups

Irene I. Bouw, Martin Möller

• We describe globally nilpotent differential operators of rank 2 defined over a number field whose monodromy group is a nonarithmetic Fuchsian group. We show that these differential operators have an S-integral solution. These differential operators are naturally associated with Teichm¨uller curves in the moduli space of curves of genus 2. They are counterexamples to conjectures by Chudnovsky�Chudnovsky and Dwork. We also determine the field of moduli of primitive Teichm¨uller curves in the moduli space of curves of genus 2, and an explicit equation in some cases.