A Gersten–Witt spectral sequence for regular schemes
Paul Balmer,Charles Walter +1 more
TLDR
In this paper, a spectral sequence whose non-zero E 1 -terms are the Witt groups of the residue fields of a regular scheme X, arranged in Gersten-Witt complexes, was constructed.Abstract:
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.read more
Citations
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Chow-Witt groups and Grothendieck-Witt groups of regular schemes
Jean Fasel,Vasudevan Srinivas +1 more
TL;DR: In this article, the authors use derived Grothendieck-Witt groups and Euler classes to detect some obstructions for P to split off a free factor of rank one.
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A cohomological classification of vector bundles on smooth affine threefolds
Aravind Asok,Jean Fasel +1 more
TL;DR: In this article, the authors give a cohomological classification of vector bundles of rank 2 on a smooth affine over an algebraically closed field having characteristic unequal to 2, and deduce that cancellation holds for rank 2 vector bundles on such varieties.
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Witt Cohomology, Mayer–Vietoris, Homotopy Invariance and the Gersten Conjecture
TL;DR: In this paper, the Gersten-Witt Conjecture for semi-local regular rings of geometric type over infinite fields of characteristic different from two was shown to hold for Witt groups of regular schemes.
Journal Article
The Chow-Witt ring.
TL;DR: In this article, a ring structure on the total Chow-Witt group of any integral smooth scheme over a field of characteristic different from 2 is defined, and the structure can be used to define a class of integral smooth schemes.
References
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Symmetric bilinear forms
John Milnor,Dale Husemoller +1 more
TL;DR: In this article, the Hasse-Minkowski Theorem and the Signature mod 8 of the Quadratic Reciprocity Theorem are used to describe the inner product spaces over a field.