Title page for ETD etd-07072008-154718


Type of Document Dissertation
Author Smith, Karli
Author's Email Address ksmith@math.lsu.edu
URN etd-07072008-154718
Title Trace Forms of Abelian Extensions of Number Fields
Degree Doctor of Philosophy (Ph.D.)
Department Mathematics
Advisory Committee
Advisor Name Title
Robert Perlis Committee Chair
Frank Neubrander Committee Member
Jimmie Lawson Committee Member
Michael Tom Committee Member
Richard Litherland Committee Member
Lynn LaMotte Dean's Representative
Keywords
  • galois
  • normal
  • witt ring
  • witt equivalence
  • symmetric bilinear forms
  • algebraic
Date of Defense 2008-07-02
Availability unrestricted
Abstract
This dissertation is concerned with providing a description of certain symmetric bilinear forms, called trace forms, associated with finite normal extensions N/K of an algebraic number field K, with abelian Galois group Gal(N/K). These abelian trace forms are described up to Witt equivalence, that is, they are described as elements in the Witt ring W(K). Complete descriptions are obtained when the base field K has exactly one dyadic prime and either no real embeddings or one real embedding. For these fields K, the set of abelian trace forms is closed under multiplication in the Witt ring W(K).
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