On the density of supercuspidal points of fixed regular weight in local deformation rings and global Hecke algebras

Matthew Emerton; Vytautas Paškūnas

doi:10.5802/jep.119

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]

Matthew Emerton ¹ ; Vytautas Paškūnas ²

¹ University of Chicago, Department of Mathematics 5734 S. University Ave., Chicago, IL 60637, United States
² Universität Duisburg-Essen, Fakultät für Mathematik Thea-Leymann-Str. 9, 45127 Essen, Germany

Journal de l’École polytechnique — Mathématiques, Tome 7 (2020), pp. 337-371.

Résumé
Abstract

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

Zbl

DOI : 10.5802/jep.119

Classification : 11S37, 22E50
Keywords: $p$-adic Hodge theory, deformation theory of Galois representations, $p$-adic automorphic forms
Mot clés : Théorie de Hodge $p$-adique, théorie des déformations des représentations galoisiennes, formes automorphes $p$-adiques

Affiliations des auteurs :

Matthew Emerton ¹ ; Vytautas Paškūnas ²

¹ University of Chicago, Department of Mathematics 5734 S. University Ave., Chicago, IL 60637, United States
² Universität Duisburg-Essen, Fakultät für Mathematik Thea-Leymann-Str. 9, 45127 Essen, Germany

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {On the density of supercuspidal points of fixed regular weight in local deformation rings and global {Hecke} algebras},
     journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
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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/articles/10.5802/jep.119/

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