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ON THE SECOND STIEFEL–WHITNEY CLASS OF SCALED TRACE FORMS OF CENTRAL SIMPLE ALGEBRAS

Published online by Cambridge University Press:  01 April 2000

ROSALI BRUSAMARELLO  and
JORGE MORALES
ROSALI BRUSAMARELLO
Affiliation:
Departamento de Matemática, Universidade Estadual de Maringá, Avenida Colombo 5790, Maringá-PR 87020-900, Brazil; [email protected]
JORGE MORALES
Affiliation:
Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA; [email protected]
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Abstract

The second Stiefel–Whitney class of the quadratic form trA/k(ax2) is computed, where A is a central simple algebra over a perfect field k of characteristic different from 2, a ∈ A is a fixed element, and trA/k is the reduced trace. 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[otimes ]kE, where E is a commutative étale algebra over k that depends on the semisimple part of a.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 61 , Issue 2 , April 2000 , pp. 335 - 348
Copyright
The London Mathematical Society 2000

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