Stable reduction of modular curves

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We determine the stable reduction at $p$ of all three point covers of the projective line with Galois group ${\rm SL}_2(p)$. As a special case, we recover the results of Deligne and Rapoport on the reduction of the modular curves $X_0(p)$ and $X_1(p)$. Our method does not use the fact that modular curves are moduli spaces. Instead, we rely on results of Raynaud and the authors which describe the stable reduction of three point covers whose Galois group is strictly divisible by $p$.
18 pages, 2 figures

Keywords

Algebraic Geometry, Number Theory, 14H30; 11G20, 14G35

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/65407

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0210363
 http://arxiv.org/abs/math/0210363

Collections

arXiv