Stark's conjectures

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dc.contributor.advisorHughes, Kenen_ZA
dc.contributor.authorMostert, Pieteren_ZA
dc.date.accessioned2016-04-20T11:10:23Z
dc.date.available2016-04-20T11:10:23Z
dc.date.issued2008en_ZA
dc.descriptionIncludes bibliographical references.en_ZA
dc.description.abstractWe give a slightly more general version of the Rubin-Stark conjecture, but show that in most cases it follows from the standard version. After covering the necessary background, we state the principal Stark conjecture and show that although the conjecture depends on a choice of a set of places and a certain isomorphism of Q[GJ-modules, it is independent of these choices. The conjecture is shown to satisfy certain 'functoriality' properties, and we give proofs of the conjecture in some simple cases. The main body of this dissertation concerns a slightly more general version of the Rubin-Stark conjecture. A number of Galois modules. Connected with the conjecture are defined in chapter 4, and some results on exterior powers and Fitting ideals are stated. In chapter 5 the Rubin-Stark conjecture is stated and we show how its truth is unaffected by lowering the top field, changing a set S of places appropriately, and enlarging moduli. We end by giving proofs of the conjecture in several cases. A number of proofs, which would otherwise have interrupted the flow of the exposition, have been relegated to the appendix, resulting in this dissertation suffering from a bad case of appendicitis.en_ZA
dc.identifier.apacitationMostert, P. (2008). <i>Stark's conjectures</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/18998en_ZA
dc.identifier.chicagocitationMostert, Pieter. <i>"Stark's conjectures."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2008. http://hdl.handle.net/11427/18998en_ZA
dc.identifier.citationMostert, P. 2008. Stark's conjectures. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Mostert, Pieter AB - We give a slightly more general version of the Rubin-Stark conjecture, but show that in most cases it follows from the standard version. After covering the necessary background, we state the principal Stark conjecture and show that although the conjecture depends on a choice of a set of places and a certain isomorphism of Q[GJ-modules, it is independent of these choices. The conjecture is shown to satisfy certain 'functoriality' properties, and we give proofs of the conjecture in some simple cases. The main body of this dissertation concerns a slightly more general version of the Rubin-Stark conjecture. A number of Galois modules. Connected with the conjecture are defined in chapter 4, and some results on exterior powers and Fitting ideals are stated. In chapter 5 the Rubin-Stark conjecture is stated and we show how its truth is unaffected by lowering the top field, changing a set S of places appropriately, and enlarging moduli. We end by giving proofs of the conjecture in several cases. A number of proofs, which would otherwise have interrupted the flow of the exposition, have been relegated to the appendix, resulting in this dissertation suffering from a bad case of appendicitis. DA - 2008 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2008 T1 - Stark's conjectures TI - Stark's conjectures UR - http://hdl.handle.net/11427/18998 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/18998
dc.identifier.vancouvercitationMostert P. Stark's conjectures. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2008 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/18998en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematics and Applied Mathematicsen_ZA
dc.titleStark's conjecturesen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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