DigitalCommons@McMaster

Title

The generalized Coates-Sinnott Conjecture for some families of cubic extensions of number fields

Author

Darren Gray

Date of Award

2009

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

Supervisor

Manfred Kolster

Language

English

Abstract

Let E/k be an S₃ extension of totally real number fields with quadratic subextension F/k. The generalized Coates-Sinnott conjecture predicts that for n ≥ 2, the integralized Stickelberger element w_n(E)θ_E/F(1-n) attached to the cyclic cubic extension E/F should annihilate the p-part of H²_Μ(Ο_E, Z(n)) for all primes p. We show this to be true for all p ≠ 2, 3.

Recommended Citation

Gray, Darren, "The generalized Coates-Sinnott Conjecture for some families of cubic extensions of number fields" (2009). Open Access Dissertations and Theses. Paper 4236.
http://digitalcommons.mcmaster.ca/opendissertations/4236

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