## Minimal resolution and stable reduction of X_{0}(N)

Annales de l'Institut Fourier, Grenoble, 40, 1, 31-67
(1990).

### Summary/Résumé

For N a positive integer, let X_{0}(N) denote the proper
model over **Z** of the modular curve associated to elliptic
curves with a given cyclic subgroup of order N, constructed by
normalization and described by Katz and Mazur in their book
on Arithmetic moduli of elliptic curves. In this paper,
we determine the minimal resolution of X_{0}(N) over
**Z**[1/6] for any N, and the stable reduction modulo a
prime p of X_{0}(p^{2}N) for all p>3 and N prime
to p.

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###### Dernière modification: 18 novembre 1998

edix@univ-rennes1.fr