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hal.structure.identifierRudjer Boskovic Institute [Zagreb]
dc.contributor.authorDUTOUR SIKIRIC, Mathieu
hal.structure.identifierInstitut Fourier [IF ]
dc.contributor.authorELBAZ-VINCENT, Philippe
hal.structure.identifierDepartment of Mathematics [Cambridge] [HARVARD]
dc.contributor.authorKUPERS, Alexander
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorMARTINET, Jacques
dc.date.accessioned2024-04-04T02:59:24Z
dc.date.available2024-04-04T02:59:24Z
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192740
dc.description.abstractEnWe enumerate the low dimensional cells in the Voronoi cell complexes attached to the modular groups $SL_N (Z)$ and $GL_N (Z)$ for $N = 8, 9, 10, 11$, using quotient sublattices techniques for $N = 8, 9$ and linear programming methods for higher dimensions. These enumerations allow us to compute some cohomology of these groups and prove that $K_8 (Z) = 0$, providing new knowledge on the Kummer-Vandiver conjecture.
dc.description.sponsorshipIDEX UGA - ANR-15-IDEX-0002
dc.language.isoen
dc.subject.enmodular groups
dc.subject.engroup cohomology
dc.subject.enVoronoi complex
dc.subject.enPerfect forms
dc.subject.enK-theory of integers
dc.subject.enwell-rounded lattices
dc.subject.enSteinberg modules
dc.subject.enlinear programming
dc.subject.enarithmetic groups
dc.subject.enKummer-Vandiver conjecture
dc.title.enVORONOI COMPLEXES IN HIGHER DIMENSIONS, COHOMOLOGY OF $GL_N (Z)$ FOR $N\ge 8$ AND THE TRIVIALITY OF $K_8 (Z)$
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Théorie des nombres [math.NT]
dc.subject.halMathématiques [math]/K-théorie et homologie [math.KT]
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-02333135
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02333135v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=DUTOUR%20SIKIRIC,%20Mathieu&ELBAZ-VINCENT,%20Philippe&KUPERS,%20Alexander&MARTINET,%20Jacques&rft.genre=preprint


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