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On the cokernel of the Witt decomposition map

Gabriele Nebe (2000)

Journal de théorie des nombres de Bordeaux

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.

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