Vincent Astier and Thomas Unger: A hermitian analogue of the Bröcker--Prestel theorem and

Submission: 2007, Jul 24

The Bröcker--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.

2000 Mathematics Subject Classification: 16K20, 11E39

Keywords and Phrases: Central simple algebras, involutions, quadratic and hermitian forms, local-global principles

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