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ON THE KERNEL OF THE BRAUER-MANIN PAIRING

dc.contributor.authorGEISSER, Thomas
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorMORIN, Baptiste
dc.date.accessioned2024-04-04T02:44:07Z
dc.date.available2024-04-04T02:44:07Z
dc.date.issued2022
dc.identifier.issn0022-314X
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191380
dc.description.abstractEnLet X be a regular scheme, flat and proper over the ring of integers of a p-adic field, with generic fiber X and special fiber X_s. We study the left kernel Br(X) of the Brauer-Manin pairing Br(X)×CH 0 (X) → Q/Z. Our main result is that the kernel of the reduction map Br(X) → Br(X_s) is the direct sum of (Q/Z[1/p])^s⊕(Q/Z)^t and a finite p-group, where s+t=ρ_{X_s}−ρ_X−I+1, for ρ_{X_s} and ρ_X the Picard numbers of X_s and X, and I the number of irreducible components of X_s. Moreover, we show that t>0 implies s>0.
dc.language.isoen
dc.publisherElsevier
dc.title.enON THE KERNEL OF THE BRAUER-MANIN PAIRING
dc.typeArticle de revue
dc.subject.halMathématiques [math]
bordeaux.journalJournal of Number Theory
bordeaux.page444-463
bordeaux.volume238
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-03429184
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03429184v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Number%20Theory&rft.date=2022&rft.volume=238&rft.spage=444-463&rft.epage=444-463&rft.eissn=0022-314X&rft.issn=0022-314X&rft.au=GEISSER,%20Thomas&MORIN,%20Baptiste&rft.genre=article


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