Regular models of modular curves in prime level over \(\mathbb{Z}^{\mathrm{ur}}_p\) (Q6613380)

In the present paper, the authors give the regular models for modular curves over \(\mathbb{Z}\) or over the maximal unramified extension \(\mathbb{Z}_p^{\text{ur}}\) of \(\mathbb{Z}_p\) associated with normalizer of split and non-split Cartan subgroups of \(\mathrm{GL}(2, \mathbb{F}_p)\) for any prime \(p\). These regular models allow them to compute the group of connected components of the fiber at \(p\) of the Néron model of the Jacobians of those curves.