| dc.contributor.advisor | Mihailescu, Preda Prof. Dr. | |
| dc.contributor.author | Müller, Katharina | |
| dc.date.accessioned | 2021-04-15T14:59:49Z | |
| dc.date.available | 2021-04-29T09:53:52Z | |
| dc.date.issued | 2021-04-15 | |
| dc.identifier.uri | http://hdl.handle.net/21.11130/00-1735-0000-0008-57F3-4 | |
| dc.identifier.uri | http://dx.doi.org/10.53846/goediss-8553 | |
| dc.language.iso | eng | de |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | |
| dc.subject.ddc | 510 | de |
| dc.title | Classical Conjectures in Iwasawa Theory for the split prime Z_p-extension and the cyclotomic Z_p-extension | de |
| dc.type | doctoralThesis | de |
| dc.contributor.referee | Mihailescu, Preda Prof. Dr. | |
| dc.date.examination | 2021-03-26 | |
| dc.description.abstracteng | This thesis constist of three parts. The first one considers the so called split prime Z_p extension over an imaginary quadratic field in which the rational prime p splits. In this setup we discuss the mu=0 conjecture as well as the main conjecture for finite abelian extensions of K. The second part of the thesis concentrates on the cyclotomic Z_p extension of a CM number field. We give a Galois theoretic interpretation of the Gross and the Gross-Kuzmin conjecture under mild assumptions on K. In the third part we specialize to the case of p=2. He we look at the capitulation problem along the cyclotomic Z_2 extension in CM fields and determine the class groups of the finite layers of the cyclotomic Z_2 extension for a certain family of biquadratic base fields. | de |
| dc.contributor.coReferee | Brüdern, Jörg Prof. Dr. | |
| dc.contributor.thirdReferee | Bley, Werner, Prof. Dr. | |
| dc.subject.eng | Iwasawa Theory | de |
| dc.subject.eng | Main Conjecture | de |
| dc.subject.eng | Gross Conjecture | de |
| dc.subject.eng | Capitulation | de |
| dc.subject.eng | Class Groups | de |
| dc.subject.eng | Z_p extensions | de |
| dc.identifier.urn | urn:nbn:de:gbv:7-21.11130/00-1735-0000-0008-57F3-4-3 | |
| dc.affiliation.institute | Fakultät für Mathematik und Informatik | de |
| dc.subject.gokfull | Mathematics (PPN61756535X) | de |
| dc.description.embargoed | 2021-04-21 | |
| dc.identifier.ppn | 1755104413 | |