CARUSO, Xavier; DAVID, Agnès; MÉZARD, Ariane

doi:10.2140/moscow.2023.12.1

Métadonnées

Licence d’utilisation du document

CARUSO, Xavier
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]

DAVID, Agnès
Laboratoire de Mathématiques de Besançon (UMR 6623) [LMB]
Institut de Recherche Mathématique de Rennes [IRMAR]

MÉZARD, Ariane
Département de Mathématiques et Applications - ENS-PSL [DMA]

Langue

Article de revue

Ce document a été publié dans

Moscow Journal of Combinatorics and Number Theory. 2023, vol. 12, n° 1, p. 1 - 56

Moscow Institute of Physics and Technology

Résumé en anglais

Let $F$ be a finite unramified extension of $\mathbb Q_p$ and $\bar\rho$ be an absolutely irreducible mod~$p$ $2$-dimensional representation of the absolute Galois group of $F$. Let $t$ be a tame inertial type of $F$. We conjecture that the deformation space parametrizing the potentially Barsotti--Tate liftings of $\bar\rho$ having type $t$ depends only on the Kisin variety attached to the situation, enriched with its canonical embedding into $(\mathbb P^1)^f$ and its shape stratification. We give evidences towards this conjecture by proving that the Kisin variety determines the cardinality of the set of common Serre weights $D(t,\bar\rho) = D(t) \cap D(\bar\rho)$. Besides, we prove that this dependance is nondecreasing (the smaller is the Kisin variety, the smaller is the number of common Serre weights) and compatible with products (if the Kisin variety splits as a product, so does the number of weights).< Réduire

URI

https://oskar-bordeaux.fr/handle/20.500.12278/191396

DOI

http://dx.doi.org/10.2140/moscow.2023.12.1

Project ANR

Correspondance de Langlands p-adique : une approche constructive et algorithmique - ANR-18-CE40-0026
Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251