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.References
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Additional Information
- William T. Sanders
- Affiliation: Department of Mathematical Sciences (IMF), Norwegian University of Science and Technology, 7491 Trondheim, Norway
- MR Author ID: 1139990
- Email: william.sanders@math.ntnu.no
- Sarang Sane
- Affiliation: Department of Mathematics, Indian Institute of Technology Madras, Sardar Patel Road, Adyar, Chennai, India 600036
- MR Author ID: 872419
- Email: sarangsanemath@gmail.com
- 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
- © Copyright 2016 American Mathematical Society
- 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
- MathSciNet review: 3624397