Continuity of total signature maps for Azumaya algebras with involution

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 earlier paper for central simple algebras can be extended to Azumaya algebras and leads to a natural way of choosing the signature of a hermitian form at a given ordering, producing total signatures of hermitian forms that are continuous functions on the real spectrum of the base ring.