Finite homological dimension and a derived equivalence

Sanders, William; Sane, Sarang

doi:10.1090/tran/6882

Finite homological dimension and a derived equivalence
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by William T. Sanders and Sarang Sane PDF

Trans. Amer. Math. Soc. 369 (2017), 3911-3935 Request permission

Abstract:

For a Cohen-Macaulay ring $R$, we exhibit the equivalence of the bounded derived categories of certain resolving subcategories, which, amongst other results, yields an equivalence of the bounded derived category of finite length and finite projective dimension modules with the bounded derived category of projective modules with finite length homologies. This yields isomorphisms of $K$-theory and Witt groups (amongst other invariants) and improves on terms of associated spectral sequences and Gersten complexes.

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