Dissertation/Thesis Abstract

On a generalization of the rank one Rubin-Stark conjecture
by Vallieres, Daniel, Ph.D., University of California, San Diego, 2011, 195; 3456772
Abstract (Summary)

This thesis is concerned with the extended abelian rank one Stark conjecture stated for the first time in Erickson’s thesis, see [19]. Here, we investigate it in more depth than has been done so far. We formulate a stronger question (Question 5.2) which seems easier to investigate both theoretically and computationally. Question 5.2 includes a generalization of the Brumer-Stark conjecture on annihilation of class groups (see Question 5.7). We link it with a conjecture of Gross and in the process find some new integrality properties of the Stickelberger element (Theorem 5.29). In order to better understand the notion of 1-cover already introduced in [19], we single out the notion of minimal cocyclic subgroups, which is purely group theoretical (Definition 4.17). Finally, using these minimal cocyclic subgroups, we provide some numerical examples with base field [special characters omitted] for which Question 5.2, and thus the extended abelian rank one Stark conjecture, have an affirmative answer (Appendix B).

Indexing (document details)
Advisor: Popescu, Cristian D.
Commitee: Caponigro, Ivano, Gan, Wee Teck, Graham, Ronald, Stark, Harold M.
School: University of California, San Diego
Department: Mathematics
School Location: United States -- California
Source: DAI-B 72/08, Dissertation Abstracts International
Subjects: Mathematics
Keywords: Extended abelian rank one Stark conjecture, Rubin-Stack conjecture, Stark conjecture
Publication Number: 3456772
ISBN: 978-1-124-66434-7
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