Deforming motivic theories I: Pure weight perfect Modules on divisorial schemes
arXiv:0803.3669
Abstract
In this paper, we introduce a notion of weight r pseudo-coherent Modules associated to a regular closed immersion i:Y -> X of codimension r, and prove that there is a canonical derived Morita equivalence between the DG-category of perfect complexes on a divisorial scheme X whose cohomological support are in Y and the DG-category of bounded complexes of weight r pseudo-coherent O_X-Modules supported on Y. The theorem implies that there is the canonical isomorphism between the Bass-Thomason-Trobaugh non-connected K-theory [TT90], [Sch06] (resp. the Keller-Weibel cyclic homology [Kel98], [Wei96]) for the immersion and the Schlichting non-connected K-theory [Sch04] associated to (resp. that of) the exact category of weight r pseudo-coherent Modules. For the connected K-theory case, this result is just Exercise 5.7 in [TT90]. As its application, we will decide on a generator of the topological filtration on the non-connected K-theory (resp. cyclic homology theory) for affine Cohen-Macaulay schemes.
References in corpus (9)
- On the cyclic homology of ringed spaces and schemes
- Transformation de Fourier generalisee
- Homotopical and Higher Categorical Structures in Algebraic Geometry
- Motivic interpretation of Milnor -groups attached to Jacobian varieties
- Remarks on 1-motivic sheaves
- Additive Chow groups of schemes
- Regulators on additive higher Chow groups
- Algebraic K-theory and abstract homotopy theory
- A Hochschild-cyclic approach to additive higher Chow cycles