3 years ago

Weakly hyperbolic involutions

Karim Johannes Becher, Thomas Unger

Publication date: March 2018

Source: Expositiones Mathematicae, Volume 36, Issue 1

Author(s): Karim Johannes Becher, Thomas Unger

Abstract

Pfister’s Local–Global Principle states that a quadratic form over a (formally) real field is weakly hyperbolic (i.e. represents a torsion element in the Witt ring) if and only if its total signature is zero. This result extends naturally to the setting of central simple algebras with involution. The present article provides a new proof of this result and extends it to the case of signatures at preorderings. Furthermore the quantitative relation between nilpotence and torsion is explored for quadratic forms as well as for central simple algebras with involution.

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