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Graded quaternion symbol equivalence of function fields

Przemysław Koprowski (2007)

Czechoslovak Mathematical Journal

We present criteria for a pair of maps to constitute a quaternion-symbol equivalence (or a Hilbert-symbol equivalence if we deal with global function fields) expressed in terms of vanishing of the Clifford invariant. In principle, we prove that a local condition of a quaternion-symbol equivalence can be transcribed from the Brauer group to the Brauer-Wall group.

Grothendieck and Witt groups in the reduced theory of quadratic forms

Andrzej Sładek (1980)

Annales Polonici Mathematici

Abstract. Let F be a formally real field. Denote by G(F) and G t ( F ) the Grothen-dieck group of quadratic forms over F and its torsion subgroup, respectively. In this paper we study the structure of the factor group G ( F ) / G t ( F ) . This reduced Grothendieck group is a free Abelian group. The main results of the paper describe some sets of generators for G ( F ) / G t ( F ) , which in many cases allow us to find a basis for the group. Throughout the paper we use the language of the reduced theory of quadratic forms. In the final part...

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