Publication:
Stark units and the main conjectures for totally real fields

dc.contributor.departmentDepartment of Mathematics
dc.contributor.kuauthorBüyükboduk, Kazım
dc.contributor.schoolcollegeinstituteCollege of Sciences
dc.date.accessioned2024-11-09T12:11:54Z
dc.date.issued2009
dc.description.abstractThe main theorem of the author’s thesis suggests that it should be possible to lift the Kolyvagin systems of Stark units, constructed in an earlier paper also by the author, to a Kolyvagin system over the cyclotomic Iwasawa algebra. In this paper, we verify that this indeed is true. This construction of Kolyvagin systems over the cyclotomic Iwasawa algebra from Stark units gives the first example towards a more systematic study of Kolyvagin system theory over an Iwasawa algebra when the core Selmer rank (in the sense of Mazur and Rubin) is greater than one. As a result of this construction, we reduce the main conjectures of Iwasawa theory for totally real fields to a statement of local Iwasawa theory, assuming the truth of the Rubin-Stark conjecture and Leopoldt’s conjecture. This statement of local Iwasawa theory turns out to be interesting in its own right as it suggests a relation between solutions to p-adic and complex Stark conjectures.
dc.description.fulltextYES
dc.description.indexedbyWOS
dc.description.indexedbyScopus
dc.description.issue5
dc.description.openaccessYES
dc.description.publisherscopeInternational
dc.description.sponsoredbyTubitakEuN/A
dc.description.versionAuthor's final manuscript
dc.description.volume145
dc.identifier.doi10.1112/S0010437X09004163
dc.identifier.eissn1570-5846
dc.identifier.embargoNO
dc.identifier.filenameinventorynoIR00026
dc.identifier.issn0010-437X
dc.identifier.quartileQ1
dc.identifier.urihttps://doi.org/10.1112/S0010437X09004163
dc.identifier.wos271300700004
dc.keywordsIwasawa theory
dc.keywordsKolyvagin systems
dc.keywordsStark conjectures
dc.language.isoeng
dc.publisherFoundation Compositio Mathematica
dc.relation.grantnoNA
dc.relation.ispartofCompositio Mathematica
dc.relation.urihttp://cdm21054.contentdm.oclc.org/cdm/ref/collection/IR/id/1057
dc.subjectMathematics
dc.titleStark units and the main conjectures for totally real fields
dc.typeJournal Article
dspace.entity.typePublication
local.contributor.kuauthorBüyükboduk, Kazım
local.publication.orgunit1College of Sciences
local.publication.orgunit2Department of Mathematics
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