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

Soit N≥1 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 p≥5 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.

Let N≥1 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 p≥5 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.

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     author = {Edixhoven, Bas},
     title = {Minimal resolution and stable reduction of $X_0(N)$},
     journal = {Annales de l'Institut Fourier},
     pages = {31--67},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {40},
     number = {1},
     year = {1990},
     doi = {10.5802/aif.1202},
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Edixhoven, Bas. Minimal resolution and stable reduction of $X_0(N)$. Annales de l'Institut Fourier, Tome 40 (1990) no. 1, pp. 31-67. doi : 10.5802/aif.1202. https://aif.centre-mersenne.org/articles/10.5802/aif.1202/

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