Geodesic
Semistable reduction of modular curves associated with maximal subgroups in prime level
Documenta mathematica, Tome 26 (2021), pp. 231-269 Cet article a éte moissonné depuis la source EMS Press

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We complete the description of semistable models for modular curves associated with maximal subgroups of GL2​(Fp​) (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 modp, 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.
DOI : 10.4171/dm/814
Classification : 11G18, 11G20, 14G35
Mots-clés : modular curves, maximal prime level subgroups, non-split Cartan, semistable models 
@article{10_4171_dm_814,
     author = {Bas Edixhoven and Pierre Parent},
     title = {Semistable reduction of modular curves associated with maximal subgroups in prime level},
     journal = {Documenta mathematica},
     pages = {231--269},
     year = {2021},
     volume = {26},
     doi = {10.4171/dm/814},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/814/}
}
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%A Pierre Parent
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%J Documenta mathematica
%D 2021
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Bas Edixhoven; Pierre Parent. Semistable reduction of modular curves associated with maximal subgroups in prime level. Documenta mathematica, Tome 26 (2021), pp. 231-269. doi: 10.4171/dm/814

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