Minimal resolution and stable reduction of X 0 (N)
Annales de l'Institut Fourier, Volume 40 (1990) no. 1, p. 31-67

Let N1 be an integer. Let X 0 (N) be the modular curve over Z, as constructed by Katz and Mazur. The minimal resolution of X 0 (N) over Z[1/6] is computed. Let p5 be a prime, such that N=p 2 M, with M prime to p. Let n=(p 2 -1)/2. It is shown that X 0 (N) has stable reduction at p over Q[p n], and the fibre at p of the stable model is computed.

Soit N1 un nombre entier. Soit X 0 (N) la courbe modulaire sur Z, construite par Katz et Mazur. On calcule la résolution minimale de X 0 (N) sur Z[1/6]. Soit p5 un nombre premier, tel que N=p 2 M, avec M premier à p. Soit n=(p 2 -1)/2. On montre que X 0 (N) a réduction stable en p sur Q[p n], et on calcule la fibre au-dessus de p du modèle stable.

@article{AIF_1990__40_1_31_0,
     author = {Edixhoven, Bas},
     title = {Minimal resolution and stable reduction of $X\_0(N)$},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {40},
     number = {1},
     year = {1990},
     pages = {31-67},
     doi = {10.5802/aif.1202},
     zbl = {0679.14009},
     mrnumber = {92f:11080},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1990__40_1_31_0}
}
Edixhoven, Bas. Minimal resolution and stable reduction of $X_0(N)$. Annales de l'Institut Fourier, Volume 40 (1990) no. 1, pp. 31-67. doi : 10.5802/aif.1202. http://www.numdam.org/item/AIF_1990__40_1_31_0/

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