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unpublished paper (F. Chemotti, J. Min´aˇc, and J. Swallow.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 Unpublished preprint.)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.
Type
Honors thesisDepartment
MathematicsPermalink
https://hdl.handle.net/10161/1276Citation
Ferguson, Jason (2009). 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.
Honors thesis, Duke University. Retrieved from https://hdl.handle.net/10161/1276.Collections
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