4 papers
A Knebusch trace formula for Azumaya algebras with involution
Vincent Astier, Thomas Unger
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 exten…
Continuity of total signature maps for Azumaya algebras with involution
Vincent Astier, Thomas Unger
In this paper we continue our investigation of signatures of hermitian forms over Azumaya algebras with involution over commutative rings. We show that the approach used in an earl…
Pfister's local-global principle for Azumaya algebras with involution
Vincent Astier, Thomas Unger
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…
Signature maps from positive cones on algebras with involution
Vincent Astier, Thomas Unger
We introduced positive cones in an earlier paper as a notion of ordering on central simple algebras with involution that corresponds to signatures of hermitian forms. In the curren…