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math.RA2025
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…
math.RA2025
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…
math.LO2025
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…