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A classification of the extensions of degree p^2 over Q_p whose normal closure is a p-extension

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorCAPUTO, Luca
dc.date.accessioned2024-04-04T02:54:14Z
dc.date.available2024-04-04T02:54:14Z
dc.date.created2006
dc.date.issued2007
dc.identifier.issn2118-8572
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192258
dc.description.abstractEnLet k be a finite extension of Q_p and E_k be the set of the extensions of degree p^2 over k whose normal closure is a p-extension. For a fixed discriminant, we show how many extensions there are in E_{Q_p} with such discriminant and we give the discriminant and the Galois group (together with its filtration of the ramification groups) of their normal closure. We show how this method can be generalized to get a classification of the extensions in E_k.
dc.language.isoen
dc.publisherSociété Arithmétique de Bordeaux
dc.subjectp-adic extensions
dc.subjectramification groups
dc.subjectdiscriminant
dc.title.enA classification of the extensions of degree p^2 over Q_p whose normal closure is a p-extension
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Théorie des nombres [math.NT]
bordeaux.journalJournal de Théorie des Nombres de Bordeaux
bordeaux.page337
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00268079
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00268079v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20de%20Th%C3%A9orie%20des%20Nombres%20de%20Bordeaux&rft.date=2007&rft.spage=337&rft.epage=337&rft.eissn=2118-8572&rft.issn=2118-8572&rft.au=CAPUTO,%20Luca&rft.genre=article


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