Combinatorics of Serre weights in the potentially Barsotti-Tate setting
hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
hal.structure.identifier | Analyse cryptographique et arithmétique [CANARI] | |
dc.contributor.author | CARUSO, Xavier | |
hal.structure.identifier | Laboratoire de Mathématiques de Besançon (UMR 6623) [LMB] | |
hal.structure.identifier | Institut de Recherche Mathématique de Rennes [IRMAR] | |
dc.contributor.author | DAVID, Agnès | |
hal.structure.identifier | Département de Mathématiques et Applications - ENS Paris [DMA] | |
dc.contributor.author | MÉZARD, Ariane | |
dc.date.accessioned | 2024-04-04T02:44:18Z | |
dc.date.available | 2024-04-04T02:44:18Z | |
dc.date.issued | 2023 | |
dc.identifier.issn | 2220-5438 | |
dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191396 | |
dc.description.abstractEn | 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). | |
dc.description.sponsorship | Correspondance de Langlands p-adique : une approche constructive et algorithmique - ANR-18-CE40-0026 | |
dc.description.sponsorship | Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020 | |
dc.language.iso | en | |
dc.publisher | Moscow Institute of Physics and Technology | |
dc.rights.uri | http://creativecommons.org/licenses/by/ | |
dc.title.en | Combinatorics of Serre weights in the potentially Barsotti-Tate setting | |
dc.type | Article de revue | |
dc.identifier.doi | 10.2140/moscow.2023.12.1 | |
dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
dc.identifier.arxiv | 2105.04147 | |
bordeaux.journal | Moscow Journal of Combinatorics and Number Theory | |
bordeaux.page | 1 - 56 | |
bordeaux.volume | 12 | |
bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
bordeaux.issue | 1 | |
bordeaux.institution | Université de Bordeaux | |
bordeaux.institution | Bordeaux INP | |
bordeaux.institution | CNRS | |
bordeaux.peerReviewed | oui | |
hal.identifier | hal-03221168 | |
hal.version | 1 | |
hal.popular | non | |
hal.audience | Internationale | |
hal.origin.link | https://hal.archives-ouvertes.fr//hal-03221168v1 | |
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