A Knebusch trace formula for Azumaya algebras with involution
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.
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