Pfister's local-global principle for Azumaya algebras with involution

2022/10/10 by Astier, Vincent, Unger, Thomas · 2 citations
#11E39 #13J30 #16H05 #16W10 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2210.04851

Abstract

We prove Pfister's local-global principle for hermitian forms over Azumaya algebras with involution over semilocal rings, and show in particular that the Witt group of nonsingular hermitian forms is 2-primary torsion. Our proof relies on a hermitian version of Sylvester's law of inertia, which is obtained from an investigation of the connections between a pairing of hermitian forms extensively studied by Garrel, signatures of hermitian forms, and positive semidefinite quadratic forms.

Cited by

• Continuity of total signature maps for Azumaya algebras with involution
• Signature maps from positive cones on algebras with involution

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