RANKS OF p-CLASS GROUPS IN CYCLIC p-EXTENSIONS OF ANTI-CYCLOTOMIC Z2-EXTENSIONS

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dc.contributor.advisorWashington, Lawrence Cen_US
dc.contributor.authorKirsch, Ariellaen_US
dc.contributor.departmentMathematicsen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2019-09-26T05:32:13Z
dc.date.available2019-09-26T05:32:13Z
dc.date.issued2019en_US
dc.description.abstractIn [1], Iwasawa proved a structure theorem for the l-class group in Zl-extensions. In this thesis, we consider instead the p-class group in Zl-extensions, particularly when l=2 and p=3. Fixing K0 =Q(i), we let L0/K0 be a cyclic degree p extension and let L∞/L0 be the lift of the anti-cyclotomic Z2-extension of K0. The rank of the ambiguous ideal class group is given by Chevalley’s formula. We study the question, does Chevalley’s formula in fact explain the entire growth in the rank of the class group? We study the ranks of the class groups of L0 and L1, proving results that give the rank of the class group when p = 3 and developing heuristics. We also consider the unit structure of Kn and prove that if a relative unit of Kn is the norm of an element in Ln modulo pth powers, then all of the relative units must be norms modulo pth powers. Additionally, we include computational results and evidence that Iwasawa’s structure theorem does not extend to the p-class group in Zl -extensions.en_US
dc.identifierhttps://doi.org/10.13016/1mwf-kpsx
dc.identifier.urihttp://hdl.handle.net/1903/24934
dc.language.isoenen_US
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pquncontrolledclass groupen_US
dc.subject.pquncontrolledIwasawa theoryen_US
dc.subject.pquncontrollednumber theoryen_US
dc.subject.pquncontrolledZp-extensionsen_US
dc.titleRANKS OF p-CLASS GROUPS IN CYCLIC p-EXTENSIONS OF ANTI-CYCLOTOMIC Z2-EXTENSIONSen_US
dc.typeDissertationen_US

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