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Relative unitary commutator calculus and applications
This note revisits localisation and patching method in the setting of
generalised unitary groups. Introducing certain subgroups of relative
elementary unitary groups, we develop relative versions of the conjugation
calculus and the commutator calculus in unitary groups, which are both more
general, and substantially easier than the ones available in the literature.
For the general linear group such relative commutator calculus has been
recently developed by the first and the third authors. As an application we
prove the mixed commutator formula, for two form ideals of a form ring. This
answers two problems posed in a paper by Alexei Stepanov and the second author.Comment: polishe
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