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Models of the group schemes of roots of unity

hal.structure.identifierLaboratoire de Mathématiques de Versailles [LMV]
dc.contributor.authorMÉZARD, Ariane
hal.structure.identifierInstitut de Mathématiques de Jussieu [IMJ]
dc.contributor.authorROMAGNY, Matthieu
hal.structure.identifierScuola Normale Superiore di Pisa [SNS]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorTOSSICI, Dajano
dc.date.accessioned2024-04-04T02:25:24Z
dc.date.available2024-04-04T02:25:24Z
dc.date.created2011-04-12
dc.date.issued2013
dc.identifier.issn0373-0956
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189883
dc.description.abstractEnLet O_K be a discrete valuation ring of mixed characteristics (0,p), with residue field k. Using work of Sekiguchi and Suwa, we construct some finite flat O_K-models of the group scheme \mu_{p^n,K} of p^n-th roots of unity, which we call Kummer group schemes. We set carefully the general framework and algebraic properties of this construction. When k is perfect and O_K is a complete totally ramified extension of the ring of Witt vectors W(k), we provide a parallel study of the Breuil-Kisin modules of finite flat models of \mu_{p^n,K}, in such a way that the construction of Kummer groups and Breuil-Kisin modules can be compared. We compute these objects for n < 4. This leads us to conjecture that all finite flat models of \mu_{p^n,K} are Kummer group schemes.
dc.language.isoen
dc.publisherAssociation des Annales de l'Institut Fourier
dc.title.enModels of the group schemes of roots of unity
dc.typeArticle de revue
dc.identifier.doi10.5802/aif.2784
dc.subject.halMathématiques [math]/Théorie des nombres [math.NT]
dc.subject.halMathématiques [math]/Géométrie algébrique [math.AG]
dc.identifier.arxiv1104.2232
bordeaux.journalAnnales de l'Institut Fourier
bordeaux.page1055-1135
bordeaux.volume63
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue3
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00672822
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00672822v1
bordeaux.COinSctx_ver=Z39.88-2004&amp;rft_val_fmt=info:ofi/fmt:kev:mtx:journal&amp;rft.jtitle=Annales%20de%20l'Institut%20Fourier&amp;rft.date=2013&amp;rft.volume=63&amp;rft.issue=3&amp;rft.spage=1055-1135&amp;rft.epage=1055-1135&amp;rft.eissn=0373-0956&amp;rft.issn=0373-0956&amp;rft.au=M%C3%89ZARD,%20Ariane&amp;ROMAGNY,%20Matthieu&amp;TOSSICI,%20Dajano&amp;rft.genre=article


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