Publication:
Deformations of Bloch groups and Aomoto dilogarithms in characteristic p

dc.contributor.departmentDepartment of Mathematics
dc.contributor.kuauthorÜnver, Sinan
dc.contributor.schoolcollegeinstituteCollege of Sciences
dc.date.accessioned2024-11-10T00:12:43Z
dc.date.issued2011
dc.description.abstractIn this paper, we study the Bloch group B-2(F[epsilon](2)) over the ring of dual numbers of the algebraic closure of the field with p elements, for a prime p >= 5. We show that a slight modification of Kontsevich's 11/2-logarithm defines a function on B-2(F[epsilon](2)). Using this function and the characteristic p version of the additive dilogarithm function that we previously defined, we determine the structure of the infinitesimal part of B-2(Ff[epsilon](2)) completely. This enables us to define invariants on the group of deformations of Aomoto dilogarithms and determine its structure. This final result might be viewed as the analog of Hilbert's third problem in characteristic p.
dc.description.indexedbyWOS
dc.description.indexedbyScopus
dc.description.issue8
dc.description.openaccessYES
dc.description.publisherscopeInternational
dc.description.sponsoredbyTubitakEuN/A
dc.description.sponsorshipDeutsche Forschungsgemeinschaft [SFB/TR45]
dc.description.sponsorshipTUBITAK[109T674] The author thanks S. Bloch and H. Esnault for mathematical discussions, H. Esnault for the invitation to University of Duisburg-Essen, and the referee for many suggestions which improved the paper. The author was supported by SFB/TR45 of the Deutsche Forschungsgemeinschaft and 109T674 of TUBITAKwhile this paper was written.
dc.description.volume131
dc.identifier.doi10.1016/j.jnt.2011.02.003
dc.identifier.issn0022-314X
dc.identifier.quartileQ2
dc.identifier.scopus2-s2.0-79953869959
dc.identifier.urihttps://doi.org/10.1016/j.jnt.2011.02.003
dc.identifier.urihttps://hdl.handle.net/20.500.14288/17700
dc.identifier.wos290071000015
dc.keywordsPolylogarithms
dc.keywordsMixed tate motives
dc.keywordsAdditive dilogarithms mixed tate motives
dc.keywordsPolylogarithms
dc.keywordsCohomology
dc.language.isoeng
dc.publisherAcademic Press Inc Elsevier Science
dc.relation.ispartofJournal of Number Theory
dc.subjectMathematics
dc.titleDeformations of Bloch groups and Aomoto dilogarithms in characteristic p
dc.typeJournal Article
dspace.entity.typePublication
local.contributor.kuauthorÜnver, Sinan
local.publication.orgunit1College of Sciences
local.publication.orgunit2Department of Mathematics
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