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Towards a function field version of Freiman's Theorem

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorBACHOC, Christine
hal.structure.identifierLaboratoire d'informatique de l'École polytechnique [Palaiseau] [LIX]
hal.structure.identifierGeometry, arithmetic, algorithms, codes and encryption [GRACE]
dc.contributor.authorCOUVREUR, Alain
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorZÉMOR, Gilles
dc.date.accessioned2024-04-04T03:08:56Z
dc.date.available2024-04-04T03:08:56Z
dc.date.issued2018
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193570
dc.description.abstractEnWe discuss a multiplicative counterpart of Freiman's 3k−4 theorem in the context of a function field F over an algebraically closed field K. Such a theorem would give a precise description of subspaces S, such that the space S^2 spanned by products of elements of S satisfies dim S^ 2 ≤ 3 dimS − 4. We make a step in this direction by giving a complete characterisation of spaces S such that dimS^2 = 2 dimS. We show that, up to multiplication by a constant field element, such a space S is included in a function field of genus 0 or 1. In particular if the genus is 1 then this space is a Riemann-Roch space.
dc.description.sponsorshipGeométrie algébrique et théorie des codes pour la cryptographie - ANR-15-CE39-0013
dc.language.isoen
dc.publisherMathOA
dc.title.enTowards a function field version of Freiman's Theorem
dc.typeArticle de revue
dc.identifier.doi10.5802/alco.19
dc.subject.halMathématiques [math]
dc.subject.halMathématiques [math]/Théorie des nombres [math.NT]
dc.subject.halMathématiques [math]/Combinatoire [math.CO]
dc.identifier.arxiv1709.00087
bordeaux.journalAlgebraic Combinatorics
bordeaux.page501-521
bordeaux.volume1
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue4
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01584034
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01584034v1
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