### Néron models and tame ramification

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Let $N\ge 1$ be an integer. Let ${X}_{0}\left(N\right)$ be the modular curve over $\mathbf{Z}$, as constructed by Katz and Mazur. The minimal resolution of ${X}_{0}\left(N\right)$ over $\mathbf{Z}[1/6]$ is computed. Let $p\ge 5$ be a prime, such that $N={p}^{2}M$, with $M$ prime to $p$. Let $n=({p}^{2}-1)/2$. It is shown that ${X}_{0}\left(N\right)$ has stable reduction at $p$ over $\mathbf{Q}\left[\sqrt[n]{p}\right]$, and the fibre at $p$ of the stable model is computed.

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