### Deforming motivic theories I Pure weight perfect Modules on divisorial schemes, by Toshiro Hiranouchi and Satoshi Mochizuki

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 cohomologically 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.

Toshiro Hiranouchi <hiranouchi@math.kyushu-u.ac.jp>

Satoshi Mochizuki <mochi81@hotmail.com>