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Stark's conjectures
Includes bibliographical references.
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| Other Authors: | |
| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2016
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| _version_ | 1867613239460757504 |
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| access_status_str | Open Access |
| author | Mostert, Pieter |
| author2 | Hughes, Ken |
| author_browse | Hughes, Ken Mostert, Pieter |
| author_facet | Hughes, Ken Mostert, Pieter |
| author_sort | Mostert, Pieter |
| collection | Thesis |
| description | Includes bibliographical references. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/18998 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:32:58.612Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2016 |
| publishDateRange | 2016 |
| publishDateSort | 2016 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/18998 Stark's conjectures Mostert, Pieter Hughes, Ken Mathematics and Applied Mathematics Includes bibliographical references. 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. 2016-04-20T11:10:23Z 2016-04-20T11:10:23Z 2008 Master Thesis Masters MSc http://hdl.handle.net/11427/18998 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Mathematics and Applied Mathematics Mostert, Pieter Stark's conjectures |
| thesis_degree_str | Master's |
| title | Stark's conjectures |
| title_full | Stark's conjectures |
| title_fullStr | Stark's conjectures |
| title_full_unstemmed | Stark's conjectures |
| title_short | Stark's conjectures |
| title_sort | stark s conjectures |
| topic | Mathematics and Applied Mathematics |
| url | http://hdl.handle.net/11427/18998 |
| work_keys_str_mv | AT mostertpieter starksconjectures |