Pure weight perfect Modules on divisorial schemes

Toshiro Hiranouchi and Satoshi Mochizuki

A chapter in Deformation Spaces, 2010, pp 75-89 from Springer

Abstract: Abstract We introduce the notion of weight for pseudo-coherent Modules on a scheme. For a divisorial scheme X and a regular closed immersion i : Y → X of codimension r, We show that there is a canonical derived Morita equivalence between the DG-category of perfect complexes on X whose cohomological supports are in Y and the DG-category of bounded complexes of weight r pseudo-coherent O X -Modules supported on Y. This implies that there is a canonical isomorphism between their K-groups (resp. cyclic homology groups). As an application, we decide a generator of the topological filtration on nonconnected K-theory (resp. cyclic homology theory) for affine Cohen-Macaulay schemes.

Keywords: Line Bundle; Short Exact Sequence; Abelian Category; Cyclic Homology; Exact Category (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-8348-9680-3_3

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DOI: 10.1007/978-3-8348-9680-3_3

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