On the classification of hermitian forms. I. Rings of algebraic integers

C. T. C. Wall

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Let $R$ be a Dedekind domain with field of fractions $K$ and $G$ a finite group. We show that, if $R$ is a ring of $p$ -adic integers, then the Witt decomposition map $δ$ between the Grothendieck-Witt group of bilinear $K G$ -modules and the one of finite bilinear $R G$ -modules is surjective. For number fields $K, δ$ is also surjective, if $G$ is a nilpotent group of odd order, but there are counterexamples for groups of even order.