A Gersten-Witt spectral sequence for regular schemes

A spectral sequence is constructed whose non-zero E-1-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. This has several immediate consequences concerning purity for Witt groups of low-dimensional schemes. We also obtain an easy proof of the Gersten Conjecture in dimension smaller than 5. The Witt groups of punctured spectra of regular local rings are also computed. (C) 2002 Editions scientifiques et medicales Elsevier SAS.