Signatures of hermitian forms and "prime ideals" of Witt groups

Abstract

In this paper a further study is made of $H$-signatures of hermitian forms, introduced previously by the authors. It is shown that a tuple of reference forms $H$ may be replaced by a single form and that the $H$-signature is invariant under Morita equivalence of algebras with involution. The "prime ideals" of the Witt group are studied, obtaining results that are analogues of the classification of prime ideals of the Witt ring by Harrison and Lorenz-Leicht. It follows that $H$-signatures canonically correspond to morphisms into the integers.