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In this paper, we introduce a notion of weight r pseudo-coherent Modulesassociated to a regular closed immersion i:Y -> X of codimension r, and provethat there is a canonical derived Morita equivalence between the DG-category ofperfect complexes on a divisorial scheme X whose cohomological support are in Yand the DG-category of bounded complexes of weight r pseudo-coherentO_X-Modules supported on Y. The theorem implies that there is the canonicalisomorphism between the Bass-Thomason-Trobaugh non-connected K-theory [TT90],[Sch06] (resp. the Keller-Weibel cyclic homology [Kel98], [Wei96]) for theimmersion and the Schlichting non-connected K-theory [Sch04] associated to(resp. that of) the exact category of weight r pseudo-coherent Modules. For theconnected K-theory case, this result is just Exercise 5.7 in [TT90]. As itsapplication, we will decide on a generator of the topological filtration on thenon-connected K-theory (resp. cyclic homology theory) for affine Cohen-Macaulayschemes.

Deforming motivic theories I: Pure weight perfect Modules on divisorial schemes