Geodesic
Semistable reduction of modular curves associated with maximal subgroups in prime level
Documenta mathematica, Tome 26 (2021), pp. 231-269.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We complete the description of semistable models for modular curves associated with maximal subgroups of $\mathrm{GL}_2 (\mathbb{F}_p )$ (for $p$ any prime, $p>5)$. That is, in the new cases of non-split Cartan modular curves and exceptional subgroups, we identify the irreducible components and singularities of the reduction $\mathrm{mod}\,\,p$, and the complete local rings at the singularities. We review the case of split Cartan modular curves. This description suffices for computing the group of connected components of the fibre at~$p$ of the Néron model of the Jacobian.
Classification : 11G18, 11G20, 14G35
Keywords: modular curves, maximal prime level subgroups, non-split Cartan, semistable models 
@article{DOCMA_2021__26__a50,
     author = {Edixhoven, Bas and Parent, Pierre},
     title = {Semistable reduction of modular curves associated with maximal subgroups in prime level},
     journal = {Documenta mathematica},
     pages = {231--269},
     publisher = {mathdoc},
     volume = {26},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a50/}
}
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Edixhoven, Bas; Parent, Pierre. Semistable reduction of modular curves associated with maximal subgroups in prime level. Documenta mathematica, Tome 26 (2021), pp. 231-269. http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a50/