Soit un nombre entier. Soit la courbe modulaire sur , construite par Katz et Mazur. On calcule la résolution minimale de sur . Soit un nombre premier, tel que , avec premier à . Soit . On montre que a réduction stable en sur , et on calcule la fibre au-dessus de du modèle stable.
Let be an integer. Let be the modular curve over , as constructed by Katz and Mazur. The minimal resolution of over is computed. Let be a prime, such that , with prime to . Let . It is shown that has stable reduction at over , and the fibre at of the stable model is computed.
@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}, pages = {31--67}, publisher = {Institut Fourier}, volume = {40}, number = {1}, year = {1990}, doi = {10.5802/aif.1202}, zbl = {0679.14009}, mrnumber = {92f:11080}, language = {en}, url = {archive.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, Tome 40 (1990) no. 1, pp. 31-67. doi : 10.5802/aif.1202. http://archive.numdam.org/item/AIF_1990__40_1_31_0/
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