On the Second Stiefel-whitney Class of Scaled Trace Forms of Central Simple Algebras
نویسندگان
چکیده
In this paper we compute the second Stiefel-Whitney class of the quadratic form trA/k(ax ), where A is a central simple algebra over a perfect field k of characteristic different from two, a ∈ A is a fixed element, and trA/k is the reduced trace. We show that this class is related on the one hand to the class of A in the Brauer group, and on the other hand to corestrictions of quaternion algebras over certain factors arising from E⊗k E, where E is a commutative étale algebra over k that depends on the semisimple part of a.
منابع مشابه
Scaled trace forms of central simple algebras
Any central simple algebra over a field of characteristic not two has a well-defined non-singular quadratic form called the trace form attached to it. This quadratic form was studied in [6] from the viewpoint of the algebraic theory of quadratic forms. In this article we examine a generalization of trace forms to “scaled trace forms” which are defined via the reduced trace map together with sca...
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