berhuy@math.univ-fcomte.fr

Submission: 2000, Apr. 10

In this paper, we give a characterization of trace forms of central simple algebras over a local field or a global field in terms of determinant and signatures. We also show a local-global principle for these trace forms. We apply these results to describe the image of the application $A\mapsto{\displaystyle{\frac{n}{2}}}[A]$, where $A$ is a central simple algebra of even degree over a local field or a global field.

1991 Mathematics Subject Classification:

Keywords and Phrases:

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