We construct a TeichmÃ¼ller curve uniformized by the Fuchsian triangle group âˆ†(m, n, âˆž) for every m < n â‰¤ âˆž. Our construction includes the TeichmÃ¼ller curves constructed by Veech and Ward as specialâ€¦ (More)

We compute the stable reduction of some Galois covers of the projective line branched at three points. These covers are constructed using Hurwitz spaces parameterizing metacyclic covers. Theâ€¦ (More)

We determine the stable reduction at p of all three point covers of the projective line with Galois group SL2(p). As a special case, we recover the results of Deligne and Rapoport on the reduction ofâ€¦ (More)

Let G = Dp be the dihedral group of order 2p, where p is an odd prime. Let k an algebraically closed field of characteristic p. We show that any action of G on the ring k[[y]] can be lifted to anâ€¦ (More)

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 anâ€¦ (More)

We study indigenous bundles in characteristic p > 0 with nilpotent p-curvature, and show that they corresponds to simpler objects which we call deformation data. We consider the existence problem ofâ€¦ (More)

In this paper we consider wildly ramified G-Galois covers of curves f : Y â†’ Pk branched at exactly one point over an algebraically closed field k of characteristic p. For G equal to Ap or PSL2(p), weâ€¦ (More)

In this paper we study the reduction of Galois covers of curves, from characteristic zero to positive characteristic. The starting point is a recent result of Raynaud, which gives a criterion forâ€¦ (More)

This paper concerns towers of curves over a finite field with many rational points, following Garciaâ€“Stichtenoth and Elkies. We present a new method to produce such towers. A key ingredient is theâ€¦ (More)