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Showing 1 to 5 of 5 for “"Motivic Cohomology"”.
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Motivic complexes and the K-theory of automorphisms
It has long been suspected that the conjectural motivic cohomology groups of a smooth variety X are related to the algebraic K-groups of X. Explicitly, it is expected that there is a spectral sequence whose terms are the motivic cohomology groups of X which converges to the algebraic K-groups of X. …
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Automorphisms and symbols in K(,2)
… K-theory today is devoted to the search for ""motivic cohomology."" This hoped-for cohomology theory of algebraic geometry should be analogous to the known singular homology groups of topology. In this work we consider Goodwillie and Lichtenbaum's candidate for motivic cohomology. For R a …
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Torsors over Simplicial Schemes
… basic results about the resulting non-abelian cohomology invariant, including an exact sequence associated to a central extension of sheaves of groups, as well as a characterization of the second sheaf cohomology group of BG with coefficients in a sheaf of abelian groups A, in terms of central …
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On the Witt groups of schemes
… are finite, and that finite generation of the motivic cohomology groups with mod 2 coefficients implies finite generation of the Witt groups. Regarding the second, we prove the Gersten conjecture for the Witt groups in the case of a local ring that is essentially smooth over a discrete …
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MOTIVIC HOCHSCHILD HOMOLOGY
… k, and let SH(S) be Morel and Voevodski's stable motivic homotopy category over S. Let R be a motivic ring spectrum in SH(S); we define the motivic Hochschild homology of R via the derived tensor product: MHH(R)=R ∧_{R ∧ R^{op}} R. This spectrum can be considered the motivic analogue of …