A Knebusch trace formula for Azumaya algebras with involution
Rings and Algebras
2026-03-06 v1
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 \'etale 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.
Keywords
Cite
@article{arxiv.2603.05364,
title = {A Knebusch trace formula for Azumaya algebras with involution},
author = {Vincent Astier and Thomas Unger},
journal= {arXiv preprint arXiv:2603.05364},
year = {2026}
}
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25 pages