Minimal resolution and stable reduction of $X_0\left(N\right)$

Edixhoven, Bas. "Minimal resolution and stable reduction of $X_0(N)$." Annales de l'institut Fourier 40.1 (1990): 31-67. <http://eudml.org/doc/74873>.

@article{Edixhoven1990,
abstract = {Let $N\ge 1$ be an integer. Let $X_0(N)$ be the modular curve over $\mathbf\{ Z\}$, as constructed by Katz and Mazur. The minimal resolution of $X_ 0(N)$ over $\mathbf\{ Z\}[1/6]$ is computed. Let $p\ge 5$ be a prime, such that $N=p^ 2M$, with $M$ prime to $p$. Let $n=(p^ 2-1)/2$. It is shown that $X_ 0(N)$ has stable reduction at $p$ over $\mathbf\{ Q\}[\@root n \of \{p\}]$, and the fibre at $p$ of the stable model is computed.},
author = {Edixhoven, Bas},
journal = {Annales de l'institut Fourier},
keywords = {modular curve; minimal resolution; stable reduction},
language = {eng},
number = {1},
pages = {31-67},
publisher = {Association des Annales de l'Institut Fourier},
title = {Minimal resolution and stable reduction of $X_0(N)$},
url = {http://eudml.org/doc/74873},
volume = {40},
year = {1990},
}

TY - JOUR
AU - Edixhoven, Bas
TI - Minimal resolution and stable reduction of $X_0(N)$
JO - Annales de l'institut Fourier
PY - 1990
PB - Association des Annales de l'Institut Fourier
VL - 40
IS - 1
SP - 31
EP - 67
AB - Let $N\ge 1$ be an integer. Let $X_0(N)$ be the modular curve over $\mathbf{ Z}$, as constructed by Katz and Mazur. The minimal resolution of $X_ 0(N)$ over $\mathbf{ Z}[1/6]$ is computed. Let $p\ge 5$ be a prime, such that $N=p^ 2M$, with $M$ prime to $p$. Let $n=(p^ 2-1)/2$. It is shown that $X_ 0(N)$ has stable reduction at $p$ over $\mathbf{ Q}[\@root n \of {p}]$, and the fibre at $p$ of the stable model is computed.
LA - eng
KW - modular curve; minimal resolution; stable reduction
UR - http://eudml.org/doc/74873
ER -