Fake CM and the Stable Model of X_0(Np^3)

We complete the determination of the stable model of $X_0(Np^3)$, $p\ge5$, $(N,p)=1$ begun in \cite{CMc} and compute the inertial action on the stable reduction of $X_0(p^3)$.

2000 Mathematics Subject Classification: Primary 11G18; Secondary 14G22, 11G07

Keywords and Phrases: stable reduction, modular curve

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