Year: 2002
Type: preprint
Abstract: 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 $p$.
Source: arXiv (Cornell University)
Authors: Bouw, Irene Ingeborg, Wewers, Stefan
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394668799