10 citations · 25 across the 13 of their papers we have counts for
15 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 extens…
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…
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…
Model completeness and quantifier elimination for (ordered) central simple algebras with involution
Vincent Astier
We show that the theories of some (ordered) central simple algebras with involution over real closed fields are model-complete or admit quantifier elimination, and characterise pos…
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…
Trichotomy for positive cones and a maximality counterexample
Vincent Astier, Thomas Unger
In [4] we developed the theory of positive cones on finite-dimensional simple algebras with involution, inspired by the classical Artin-Schreier theory of orderings on fields, and…
Galois extensions, positive involutions and an application to unitary space-time coding
Vincent Astier, Thomas Unger
We show that under certain conditions every maximal symmetric subfield of a central division algebra with positive unitary involution will be a Galois extension of the fixe…
Positive cones and gauges on algebras with involution
Vincent Astier, Thomas Unger
We extend the classical links between valuations and orderings on fields to Tignol-Wadsworth gauges and positive cones on finite-dimensional simple algebras with involution. We als…
Signatures, sums of hermitian squares and positive cones on algebras with involution
Vincent Astier, Thomas Unger
We provide a coherent picture of our efforts thus far in extending real algebra and its links to the theory of quadratic forms over ordered fields in the noncommutative direction,…
Positive cones on algebras with involution
Vincent Astier, Thomas Unger
We introduce positive cones on algebras with involution. These allow us to prove analogues of Artin's solution to Hilbert's 17th problem, the Artin-Schreier theorem characterizing…
Signatures of hermitian forms, positivity, and an answer to a question of Procesi and Schacher
Vincent Astier, Thomas Unger
Using the theory of signatures of hermitian forms over algebras with involution, developed by us in earlier work, we introduce a notion of positivity for symmetric elements and pro…
Stability index for algebras with involution
Vincent Astier, Thomas Unger
In earlier work we developed the theory of signatures of hermitian forms over algebras with involution with respect to orderings on the base field of the algebra and obtained in pa…
Signatures of hermitian forms and "prime ideals" of Witt groups
Vincent Astier, Thomas Unger
In this paper a further study is made of -signatures of hermitian forms, introduced previously by the authors. It is shown that a tuple of reference forms may be replaced by…
Signatures of hermitian forms and the Knebusch Trace Formula
Vincent Astier, Thomas Unger
Signatures of quadratic forms have been generalized to hermitian forms over algebras with involution. In the literature this is done via Morita theory, which causes sign ambiguitie…
A hermitian analogue of the Broecker-Prestel theorem
Vincent Astier, Thomas Unger
The Broecker-Prestel local-global principle characterizes weak isotropy of quadratic forms over a formally real field in terms of weak isotropy over the henselizations and isotropy…