A Knebusch trace formula for Azumaya algebras with involution

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Vincent Astier, Thomas Unger
DOI: 10.48550/arxiv.2603.05364
Cited by: 0
References: 2

Abstract

We establish a trace formula for signatures of hermitian forms over Azumaya algebras with involution, extending Knebusch's work on symmetric bilinear forms over finite étale extensions of commutative base rings. As an application when the base ring is semilocal, we obtain an exact sequence for total signatures, related to Pfister's local-global principle and the notion of stability index.

Fields of Study & Subjects

Advanced Algebra and Geometry Algebraic Geometry and Number Theory Rings Modules and Algebras

Publication details

Journal / source
arXiv (Cornell University)
Publication date
5 March 2026
Language
EN
Document type
Preprint