2009/06/09 by Irene I. Bouw, Bouw, Irene I., Brian Osserman +1
Computer Science · Mathematics · #11G20 #14D15 #14H37 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Cryptography and Residue Arithmetic #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #math.AG #math.NT #msc:11G20 #msc:14D15 #msc:14H37
paper · pdf · doi:10.48550/arxiv.0906.1793
23 pages
arxiv created 2009/06/09 · openalex publication_date 2009/06/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we compute the number of covers of curves with given branch behavior in characteristic p for one class of examples with four branch points and degree p. Our techniques involve related computations in the case of three branch points, and allow us to conclude in many cases that for a particular choice of degeneration, all the covers we consider degenerate to separable (admissible) covers. Starting from a good understanding of the complex case, the proof is centered on the theory of stable reduction of Galois covers.