Minimal resolution and stable reduction of X0(N)

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


For N a positive integer, let X0(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 X0(N) over Z[1/6] for any N, and the stable reduction modulo a prime p of X0(p2N) for all p>3 and N prime to p.

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Dernière modification: 18 novembre 1998