Construction of 2-ADIC Galois extension with wild inertia given by an extra special 2-group

Publication Type dissertation
School or College College of Science
Department Mathematics
Author Kocs, Christopher
Title Construction of 2-ADIC Galois extension with wild inertia given by an extra special 2-group
Date 2012-08
Description Given any field F and an odd integer n, suppose K be a degree 2n1 multiquadratic extension of F. We consider the conditions under which there is a Galois extension E of F such that Gal(E/F) is a particular extra special 2-group T0 { namely, the multiplicative group generated by basis elements of the even Clifford algebra associated with the quadratic form X2 1 + ::: + X2 n. These conditions can be restated in terms of the Weil index, which can be computed explicitly as a Gauss sum when F = Q2n. We prove an equidistribution of Gauss sums for quadratic characters on Q2n of conductor 4Z2n. As a consequence, we prove that, when n is an odd prime greater than 3, there exists a Galois extension K of Q2 such that K is a multiquadratic extension of Q2n that admits a quadratic extension E such that Gal(E/F) = T0.
Type Text
Publisher University of Utah
Subject 2-adic field extensions; Clifford algebra; Elliptic curve; Extra special 2-group; Galois theory; Quadratic forms
Subject LCSH Galois cohomology
Dissertation Institution University of Utah
Dissertation Name Doctor of Philosophy
Language eng
Rights Management Copyright © Christopher Kocs 2012
Format Medium application/pdf
Format Extent 393,300 bytes
Identifier etd3/id/1848
Source Original in Marriott Library Special Collections, QA3.5 2012 .K63
ARK ark:/87278/s63t9z0q
Setname ir_etd
Date Created 2012-08-20
Date Modified 2017-10-02
ID 195536
Reference URL https://collections.lib.utah.edu/details?id=195536
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