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arXiv · 2210.04851

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

Vincent Astier·Thomas Unger
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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.

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Vincent Astier, Thomas Unger. 2022-10-10. Pfister's local-global principle for Azumaya algebras with involution. https://doi.org/10.4171/dm/1026

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