A Gersten-witt Spectral Sequence for Regular Schemes

نویسنده

  • CHARLES WALTER
چکیده

A spectral sequence is constructed whose nonzero E1-terms are the Witt groups of the residue fields of a regular scheme X, arranged in Gersten-Witt complexes, and whose limit is the four global Witt groups of X. There are several immediate consequences concerning purity for Witt groups of low-dimensional schemes. The Witt groups of punctured spectra of regular local rings are also computed. Let X be a regular integral separated noetherian scheme in which 2 is everywhere invertible. (We will maintain these hypotheses throughout the introduction.) It is now known to the experts that the Witt groups of the residue fields of X form a nonexact cochain complex

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تاریخ انتشار 2002