Rationally but not integrally isometric bilinear forms

Abstract

Let K be a non-dyadic local field and A its ring of integers. First we notice that the classification of unimodular A-bilinear forms and of systems of two unimodular symmetric A-bilinear forms are both reduced to the classification of hermitian forms over the category of double isomorphisms over projective A-modules ; the duality is nevertheless different for each case. Then we use the methods of reduction and transfer to construct some examples of non isometric unimodular forms (or system of unimodular symmetric forms) having the same asymmetry and becoming isometric over K.