Amit Kulshrestha: Strongly anisotropic involutions on central simple algebras

Submission: 2007, Jul 23

The classical theorem of Bröcker and Prestel on quadratic forms over formally real fields determines a valuation theoretic condition under which all totally indefinite forms are weakly isotropic. In this paper, we look for analogues of such results in a more general setting of algebras with involutions. We prove that for involutions of first kind over central simple algebras of index two, one indeed has a Bröcker-Prestel like statement. The connection between two conditions, namely total indefiniteness and weak isotropicity is made via so called gauge functions on central simple algebras.

2000 Mathematics Subject Classification: 16W60, 16W10, 11E39

Keywords and Phrases: strongly anisotropic involutions, Bröcker-Prestel Theorem

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