An Artin-Schreier-type theory for signatures of hermitian forms over involutions

Abstract

In the case of quadratic forms over a field, it is well-known that the prime spectrum of the Witt ring and the space of orderings of the field determine one another, through associated signature maps. We show that a sililar relation holds for hermitian forms over algebras with involution of the first kind, replacing the usual Witt ring with the mixed Witt ring of such an algebra.

15 pages. arXiv admin note: substantial text overlap with arXiv:1903.07255