Divisible subgroups of Brauer groups and trace forms of central simple algebras
Copyright policy )Divisible subgroups of Brauer groups and trace forms of central simple algebras
Let F be a field of characteristic different from 2 and assume that F satisfies the strong approximation theorem on orderings ( F is a SAP field) and that I^3(F) is torsion-free. We prove that the 2-primary component of the torsion subgroup of the Brauer group of F is a divisible group and we prove a structure theorem on the 2-primary component of the Brauer group of F . This result generalizes well-known results for algebraic number fields. We apply these results to characterize the trace form of a central simple algebra over such a field in terms of its determinant and signatures.
local-global principle, global fields, Galois cohomology, SAP-fields, Witt rings, quadratic forms, Brauer groups (algebraic aspects), central simple algebras, strong approximation property, Algebraic theory of quadratic forms; Witt groups and rings, trace forms, Quadratic forms over general fields, Valuations, completions, formal power series and related constructions (associative rings and algebras), Brauer groups
local-global principle, global fields, Galois cohomology, SAP-fields, Witt rings, quadratic forms, Brauer groups (algebraic aspects), central simple algebras, strong approximation property, Algebraic theory of quadratic forms; Witt groups and rings, trace forms, Quadratic forms over general fields, Valuations, completions, formal power series and related constructions (associative rings and algebras), Brauer groups
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