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A Gersten-Witt complex for hermitian Witt groups of coherent algebras over schemes II: Involution of the second kind

Published online by Cambridge University Press:  04 September 2008

Stefan Gille
Stefan Gille
Affiliation:
gille@mathematik.uni-muenchen.deMathematisches InstitutUniversität MünchenTheresienstrasse 3980333 MünchenGermany
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Abstract

Let X be a regular noetherian scheme of finite Krull dimension with involution σ and an Azumaya algebra over X with involution τ of the second kind with respect to σ. We construct a hermitian and a skew-hermitian Gersten-Witt complex for (, τ) and show that these complexes are exact if X = Spec R is the spectrum of a regular semilocal ring R of geometric type, such that R is a quadratic étale extension of the fixed ring of σ.

Keywords

Azumaya algebrasWitt groups of hermitian forms
Type
Research Article
Information
Journal of K-Theory , Volume 4 , Issue 2 , October 2009 , pp. 347 - 377
Copyright
Copyright © ISOPP 2009

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