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Finite homological dimension and a derived equivalence


Authors: William T. Sanders and Sarang Sane
Journal: Trans. Amer. Math. Soc. 369 (2017), 3911-3935
MSC (2010): Primary 13D09; Secondary 13H10, 18E30, 18G35, 19D99, 19G38
DOI: https://doi.org/10.1090/tran/6882
Published electronically: November 16, 2016
MathSciNet review: 3624397
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

William T. Sanders
Affiliation: Department of Mathematical Sciences (IMF), Norwegian University of Science and Technology, 7491 Trondheim, Norway
Email: william.sanders@math.ntnu.no

Sarang Sane
Affiliation: Department of Mathematics, Indian Institute of Technology Madras, Sardar Patel Road, Adyar, Chennai, India 600036
Email: sarangsanemath@gmail.com

DOI: https://doi.org/10.1090/tran/6882
Keywords: Derived categories, finite projective dimension, finite length, resolving subcategories, Cohen-Macaulay rings, $K$-theory, derived Witt groups, Gersten complexes
Received by editor(s): June 11, 2014
Received by editor(s) in revised form: May 23, 2015
Published electronically: November 16, 2016
Additional Notes: The second named author was partially supported by the DST-INSPIRE grant number DST/INSPIRE/04/2013/000020 and IITM-NFIG grant number MAT/15-16/832/NFIG/SARA
Article copyright: © Copyright 2016 American Mathematical Society