Witt groups
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General Introduction
See also Motivic homotopy theory
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Search results
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Online References
Witt cohomology and the Gersten Conjecture, by Paul Balmer: K0433
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Paper References
Balmer: Witt groups (Chapter in the K-theory handbook, volume 2).
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Definition
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Properties
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Standard theorems
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Open Problems
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Connections to Number Theory
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Computations and Examples
The Witt groups of spheres away from two, by Ivo Dell'Ambrogio and Jean Fasel: K0769
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History and Applications
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Some Research Articles
Must add Ostvaer-Roendigs article on some spectral sequence for slices of integral Witt theory, possibly giving a new proof of the Milnor conjecture.
Zibrowius: Witt groups of curves and surfaces: http://front.math.ucdavis.edu/1110.1879
Pairings in triangular Witt theory, by Stefan Gille and Alexander Nenashev
Old thing by Balmer
An example by Totaro
Otherwise, search for Balmer at K-theory archive and the arXiv. Will not add all references here.
[arXiv:1212.5780] On the relation of special linear algebraic cobordism to Witt groups from arXiv Front: math.KT by Alexey Ananyevskiy We reconstruct derived Witt groups via special linear algebraic cobordism. There is a morphism g: MSL^{,} -> W^* of ring cohomology theories which sends the canonical Thom class th^{MSL} to the Thom class th^{W}. We show that for every smooth variety X this morphism induces an isomorphism between MSL^{,}(X)/(h -1) with the "extended" coefficient ring MSL^{4,2}(pt) -> W^{2}(pt) and derived Witt groups W^(X), where h is the stable Hopf map. This result is an analogue of the result by Panin and Walter reconstructing hermitian K-theory using symplectic algebraic cobordism.
Stabilization of the Witt Group, by Max Karoubi: Using an idea due to R. Thomason, we define a "homology theory" on the category of rings which satisfies excision, exactness, homotopy (in the algebraic sense) and periodicity of order 4. For regular noetherian rings, we find P. Balmers's higher Witt groups. For more general rings, this homology is isomorphic to the KT-theory of J. Hornbostel, inspired by the work of B. Williams. For real or complex C*-algebras, we recover - up to 2 torsion - topological K-theory. K0757
Projective push-forwards in the Witt theory of algebraic varieties, by Alexander Nenashev: K0848
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Other Information
People to ask: Baptiste Calmes, Paul Balmer
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