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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 of the modular curves X0(p) and X1(p). Our method does not use the fact that modular curves are moduli spaces. Instead, we rely on results of Raynaud and the… (More)

- IRENE I. BOUW
- 2001

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. The reduction is determined by a certain hypergeometric differential equation. This generalizes the result of Deligne and Rapoport on the reduction of the modular curve X… (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 an action on R[[y]], where R is some complete discrete valuation ring with residue field k and fraction field of characteristic 0. 2000 Mathematics subject… (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 of a certain class of deformation data, which arise from the reduction of Belyi maps from characteristic zero to characteristic p. Mathematics Subject… (More)

In this paper we consider wildly ramified G-Galois covers of curves f : Y → Pk branched at exactly one point over an algebraically closed field k of characteristic p. For G equal to Ap or PSL2(p), we prove Abhyankar’s Inertia Conjecture that all possible inertia groups occur over infinity for such covers f . In addition, we prove that the set of conductors… (More)

Let X be a generic curve of genus g defined over an algebraically closed field k of characteristic p ≥ 0. We show that for n sufficiently large there exists a tame rational map f : X → P1k with monodromy group An. This generalizes a result of Magaard–Völklein to positive characteristic.

- IRENE I. BOUW
- 2008

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 Teichmüller curves in genus 2. They are counterexamples to conjectures by… (More)

- Sabine Kampf, Martin Bossert, Irene I. Bouw
- 2011 IEEE International Symposium on Information…
- 2011

This paper presents a division algorithm to solve the key equation for Hermitian codes, which is capable of locating most error patterns with weight up to half the designed minimum distance. The algorithm has a structure similar to the Euclidean algorithm used in the decoding of Reed-Solomon codes, yet it is a little more complex because bivariate… (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 for good reduction for covers of the projective line branched at three points. We use the ideas of Raynaud to study the case of covers of the projective line branched… (More)

This paper concerns towers of curves over a finite field with many rational points, following Garcia–Stichtenoth and Elkies. We present a new method to produce such towers. A key ingredient is the study of algebraic solutions to Fuchsian differential equations modulo p. We apply our results to towers of modular curves, and find new asymptotically good… (More)