Volume no :8, Issue no: 1-2, September and December (2012)

Journal of Algebra, Number Theory: Advances and Applications

TRACE FORMS OF ABELIAN EXTENSIONS OF NUMBER FIELDS OF TYPE (1, 1)

Author's: KARLI MORRIS
Pages: [57] - [80]
Received Date: October 9, 2012
Submitted by:

Abstract

This article is concerned with describing bilinear trace forms associated with finite abelian extensions of an algebraic number field K. These abelian trace forms are described up to Witt equivalence, that is, they are described as elements in the Witt ring When the base field K has exactly one dyadic prime and one real embedding, it is shown that the Witt class of every abelian trace form over K is a product of Witt classes of eight specified types.

Keywords

trace forms, Witt ring, Witt equivalence, symmetric bilinear forms.