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Pure weight perfect Modules on divisorial schemes

In: Deformation Spaces

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  • 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 : 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.

Suggested Citation

  • Toshiro Hiranouchi & Satoshi Mochizuki, 2010. "Pure weight perfect Modules on divisorial schemes," Springer Books, in: Hossein Abbaspour & Matilde Marcolli & Thomas Tradler (ed.), Deformation Spaces, pages 75-89, Springer.
    • Handle: RePEc:spr:sprchp:978-3-8348-9680-3_3
    DOI: 10.1007/978-3-8348-9680-3_3
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