The Galois Cohomology of Square-Classes of Units in Klein-Four Group Extensions of Characteristic Not Two: A Thesis Submitted to the Department of Mathematics for Honors

Abstract

This report is an expository article that gathers and proves some of the results of a certain unpublished paper (F. Chemotti, J. Min´aˇc, and J. Swallow. Galois module structure of square classes of units of Klein 4-group extensions. April 2006. Unpublished preprint.) co-authored by Prof. John Swallow of Davidson College. For this paper, I assume familiarity with abstract algebra at the level of MATH 251 and point-set topology at the level of MATH 205. I also assume the reader has had some experience with infinite Galois theory; cohomology of profinite groups; operations on the cohomology of profinite groups, including conjugation, inflation, corestriction, and cup-product; Kummer theory; and Brauer groups. However, all of these latter topics will be quickly reviewed within this report in Chapter 3.