Non unimodular Hermitian forms (Q1909570)

The authors prove that the category of \(\varepsilon\)-Hermitian forms on the category \(M\) of finitely generated reflexive left \(A\)-modules is equivalent to the category of unimodular \(\varepsilon\)-Hermitian forms on the category of morphisms of \(M\). This allows them to reduce classification problems of non-unimodular forms to those ones of unimodular forms. Applying the described method they classify symmetric bilinear forms of given determinant over a principal ideal domain, prove the Witt cancellation theorem for \(\varepsilon\)-Hermitian forms and generalize the Springer theorem.