On the density of supercuspidal points of fixed regular weight in local deformation rings and global Hecke algebras
[Sur la densité des points supercuspidaux de poids régulier fixé dans des anneaux locaux de déformations et des algèbres de Hecke globales]
Journal de l'École polytechnique — Mathématiques, Tome 7 (2020) , pp. 337-371.

Nous étudions la clôture de Zariski, dans l’espace des déformations d’une représentation galoisienne locale, des points fermés correspondant à des représentations potentiellement semi-stables avec des propriétés de théorie de Hodge p-adique prescrites. Nous montrons, dans les cas favorables, que la clôture contient une réunion de composantes irréductibles de l’espace des déformations. Nous étudions aussi une question analogue pour les algèbres de Hecke globales.

We study the Zariski closure in the deformation space of a local Galois representation of the closed points corresponding to potentially semi-stable representations with prescribed p-adic Hodge-theoretic properties. We show in favourable cases that the closure contains a union of irreducible components of the deformation space. We also study an analogous question for global Hecke algebras.

Reçu le : 2018-11-09
Accepté le : 2020-01-16
Publié le : 2020-03-06
DOI : https://doi.org/10.5802/jep.119
Classification : 11S37,  22E50
Mots clés: Théorie de Hodge p-adique, théorie des déformations des représentations galoisiennes, formes automorphes p-adiques
@article{JEP_2020__7__337_0,
     author = {Matthew Emerton and Vytautas Pa\v sk\=unas},
     title = {On the density of supercuspidal points of fixed regular weight in local deformation rings and global Hecke algebras},
     journal = {Journal de l'\'Ecole polytechnique --- Math\'ematiques},
     publisher = {\'Ecole polytechnique},
     volume = {7},
     year = {2020},
     pages = {337-371},
     doi = {10.5802/jep.119},
     language = {en},
     url = {jep.centre-mersenne.org/item/JEP_2020__7__337_0/}
}
Matthew Emerton; Vytautas Paškūnas. On the density of supercuspidal points of fixed regular weight in local deformation rings and global Hecke algebras. Journal de l'École polytechnique — Mathématiques, Tome 7 (2020) , pp. 337-371. doi : 10.5802/jep.119. https://jep.centre-mersenne.org/item/JEP_2020__7__337_0/

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