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Towards a function field version of Freiman's Theorem
hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
dc.contributor.author | BACHOC, Christine | |
hal.structure.identifier | Laboratoire d'informatique de l'École polytechnique [Palaiseau] [LIX] | |
hal.structure.identifier | Geometry, arithmetic, algorithms, codes and encryption [GRACE] | |
dc.contributor.author | COUVREUR, Alain | |
hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
dc.contributor.author | ZÉMOR, Gilles | |
dc.date.accessioned | 2024-04-04T03:08:56Z | |
dc.date.available | 2024-04-04T03:08:56Z | |
dc.date.issued | 2018 | |
dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193570 | |
dc.description.abstractEn | We 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.sponsorship | Geométrie algébrique et théorie des codes pour la cryptographie - ANR-15-CE39-0013 | |
dc.language.iso | en | |
dc.publisher | MathOA | |
dc.title.en | Towards a function field version of Freiman's Theorem | |
dc.type | Article de revue | |
dc.identifier.doi | 10.5802/alco.19 | |
dc.subject.hal | Mathématiques [math] | |
dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
dc.subject.hal | Mathématiques [math]/Combinatoire [math.CO] | |
dc.identifier.arxiv | 1709.00087 | |
bordeaux.journal | Algebraic Combinatorics | |
bordeaux.page | 501-521 | |
bordeaux.volume | 1 | |
bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
bordeaux.issue | 4 | |
bordeaux.institution | Université de Bordeaux | |
bordeaux.institution | Bordeaux INP | |
bordeaux.institution | CNRS | |
bordeaux.peerReviewed | oui | |
hal.identifier | hal-01584034 | |
hal.version | 1 | |
hal.popular | non | |
hal.audience | Internationale | |
hal.origin.link | https://hal.archives-ouvertes.fr//hal-01584034v1 | |
bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Algebraic%20Combinatorics&rft.date=2018&rft.volume=1&rft.issue=4&rft.spage=501-521&rft.epage=501-521&rft.au=BACHOC,%20Christine&COUVREUR,%20Alain&Z%C3%89MOR,%20Gilles&rft.genre=article |
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