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}, volume = {40}, year = {1990}, pages = {31-67}, doi = {10.5802/aif.1202}, mrnumber = {92f:11080}, zbl = {0679.14009}, language = {en}, url = {http://dml.mathdoc.fr/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) pp. 31-67. doi : 10.5802/aif.1202. http://gdmltest.u-ga.fr/item/AIF_1990__40_1_31_0/
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