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Pure weight perfect Modules on divisorial schemes

  • Toshiro Hiranouchi
  • Satoshi Mochizuki

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 : YX 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 
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© Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH 2010

Authors and Affiliations

  • Toshiro Hiranouchi
  • Satoshi Mochizuki

There are no affiliations available

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