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FINITE HOMOLOGICAL DIMENSION AND A DERIVED EQUIVALENCE.

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Title: FINITE HOMOLOGICAL DIMENSION AND A DERIVED EQUIVALENCE.
Authors: SANDERS, WILLIAM T.1 william.sanders@math.ntnu.no, SANE, SARANG2 sarangsanemath@gmail.com
Source: Transactions of the American Mathematical Society. Jun2017, Vol. 369 Issue 6, p3911-3935. 25p.
Subject Terms: *Spectral sequences (Mathematics), *Mathematical complexes, *Homology theory, *Dimension theory (Algebra), *Mathematical category theory, *Witt group
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. [ABSTRACT FROM AUTHOR]
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  Data: FINITE HOMOLOGICAL DIMENSION AND A DERIVED EQUIVALENCE.
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  Data: <searchLink fieldCode="JN" term="%22Transactions+of+the+American+Mathematical+Society%22">Transactions of the American Mathematical Society</searchLink>. Jun2017, Vol. 369 Issue 6, p3911-3935. 25p.
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  Data: *<searchLink fieldCode="DE" term="%22Spectral+sequences+%28Mathematics%29%22">Spectral sequences (Mathematics)</searchLink><br />*<searchLink fieldCode="DE" term="%22Mathematical+complexes%22">Mathematical complexes</searchLink><br />*<searchLink fieldCode="DE" term="%22Homology+theory%22">Homology theory</searchLink><br />*<searchLink fieldCode="DE" term="%22Dimension+theory+%28Algebra%29%22">Dimension theory (Algebra)</searchLink><br />*<searchLink fieldCode="DE" term="%22Mathematical+category+theory%22">Mathematical category theory</searchLink><br />*<searchLink fieldCode="DE" term="%22Witt+group%22">Witt group</searchLink>
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  Data: 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. [ABSTRACT FROM AUTHOR]
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        Value: 10.1090/tran/6882
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        Text: English
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        Type: general
      – SubjectFull: Mathematical complexes
        Type: general
      – SubjectFull: Homology theory
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      – SubjectFull: Dimension theory (Algebra)
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      – SubjectFull: Mathematical category theory
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      – SubjectFull: Witt group
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      – TitleFull: FINITE HOMOLOGICAL DIMENSION AND A DERIVED EQUIVALENCE.
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            NameFull: SANDERS, WILLIAM T.
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              M: 06
              Text: Jun2017
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              Y: 2017
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