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

摘要

Let X be a regular noetherian scheme of finite Krull dimension with involutiona and A an Azumaya algebra over X with involution r of the second kind withrespect to a. We construct a hermitian and a skew-hermitian Gersten-Wittcomplex for (A, τ) and show that these complexes are exact ifX =SpecRisthe spectrum of a regular semilocal ring R of geometric type, such that R is aquadratic etale extension of the fixed ring of a.