Irene I. Bouw

The p-Rank of Ramified Covers of Curves

In this paper we study the p-rank of Abelian prime-to-p covers of the generic r-pointed curve of genus g. There is an obvious bound on the p-rank of the cover. We show that it suffices to compute the p-rank of cyclic prime-to-p covers of the generic r-pointed curve of genus zero. In that situation, we show that, for large p, the p-rank of the cover is equal to the bound.

The local lifting problem for dihedral groups

Let

Differential equations associated with nonarithmetic Fuchsian groups

G=D_p

Stable Reduction of Modular Curves

be the dihedral group of order

COMPUTING L-FUNCTIONS AND SEMISTABLE REDUCTION OF SUPERELLIPTIC CURVES

2p

Reduction of the Hurwitz space of metacyclic covers

, where

Deformation data, Belyi maps, and the local lifting problem

p

Asymptotically good towers and differential equations

is an odd prime. Let

Solving the key equation for Hermitian codes with a division algorithm

k

Indigenous bundles with nilpotent p-curvature

an algebraically closed field of characteristic