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Combinatorics of Serre weights in the potentially Barsotti-Tate setting

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierLithe and fast algorithmic number theory [LFANT]
hal.structure.identifierAnalyse cryptographique et arithmétique [CANARI]
dc.contributor.authorCARUSO, Xavier
hal.structure.identifierLaboratoire de Mathématiques de Besançon (UMR 6623) [LMB]
hal.structure.identifierInstitut de Recherche Mathématique de Rennes [IRMAR]
dc.contributor.authorDAVID, Agnès
hal.structure.identifierDépartement de Mathématiques et Applications - ENS Paris [DMA]
dc.contributor.authorMÉZARD, Ariane
dc.date.accessioned2024-04-04T02:44:18Z
dc.date.available2024-04-04T02:44:18Z
dc.date.issued2023
dc.identifier.issn2220-5438
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191396
dc.description.abstractEnLet $F$ 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.sponsorshipCorrespondance de Langlands p-adique : une approche constructive et algorithmique - ANR-18-CE40-0026
dc.description.sponsorshipCentre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020
dc.language.isoen
dc.publisherMoscow Institute of Physics and Technology
dc.rights.urihttp://creativecommons.org/licenses/by/
dc.title.enCombinatorics of Serre weights in the potentially Barsotti-Tate setting
dc.typeArticle de revue
dc.identifier.doi10.2140/moscow.2023.12.1
dc.subject.halMathématiques [math]/Théorie des nombres [math.NT]
dc.identifier.arxiv2105.04147
bordeaux.journalMoscow Journal of Combinatorics and Number Theory
bordeaux.page1 - 56
bordeaux.volume12
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue1
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-03221168
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03221168v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Moscow%20Journal%20of%20Combinatorics%20and%20Number%20Theory&rft.date=2023&rft.volume=12&rft.issue=1&rft.spage=1%20-%2056&rft.epage=1%20-%2056&rft.eissn=2220-5438&rft.issn=2220-5438&rft.au=CARUSO,%20Xavier&DAVID,%20Agn%C3%A8s&M%C3%89ZARD,%20Ariane&rft.genre=article


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