Abstract

Consider a non-Galois cubic extension K/Q ramified at a single prime p > 3. We show that if K is a subfield of an S_4-extension L/Q ramified only at p, we can determine the Artin conductor of the projective representation associated to L/Q, which is based on whether or not K/Q is totally real. We also show that the number of S_4-extensions of this type with K as a subfield is of the form 2^n - 1 for some n >= 0. If K/Q is totally real, n > 1. This proves two conjectures of Siman Wong.

Degree

MS

College and Department

Physical and Mathematical Sciences; Mathematics

Rights

http://lib.byu.edu/about/copyright/

Date Submitted

2015-06-01

Document Type

Thesis

Handle

http://hdl.lib.byu.edu/1877/etd7889

Keywords

octahedral, Galois representations, number fields

Included in

Mathematics Commons

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