A hermitian analogue of the Broecker-Prestel theorem

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Astier, Vincent
Unger, Thomas
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Abstract
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The Broecker-Prestel local-global principle characterizes weak isotropy of quadratic forms over a formally real field in terms of weak isotropy over the henselizations and isotropy over the real closures of that field. A hermitian analogue of this principle is presented for algebras of index at most two. An improved result is also presented for algebras with a decomposable involution, algebras of pythagorean index at most two, and algebras over SAP and ED fields.
Comment: Final pre-publication version
Keywords
Mathematics - Rings and Algebras, 16K20, 11E39
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