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Extended Local Cohomology and Local Homology

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Abstract

We present an in-depth exploration of the module structures of local (co)homology modules (moreover, for complexes) over the completion \(\widehat {R}^{\mathcal {a}}\) of a commutative noetherian ring R with respect to a proper ideal \(\mathcal {a}\). In particular, we extend Greenlees-May Duality and MGM Equivalence to track behavior over \(\widehat {R}^{\mathcal {a}}\), not just over R. We apply this to the study of two recent versions of homological finiteness for complexes, and to certain isomorphisms, with a view toward further applications. We also discuss subtleties and simplifications in the computations of these functors.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Clemson University, O-110 Martin Hall, Box 340975, Clemson, SC, 29634, USA

    Sean Sather-Wagstaff

  2. Mathematics and Physics Department, MacMurray College, 447 East College Ave., Jacksonville, IL, 62650, USA

    Richard Wicklein

Authors
  1. Sean Sather-Wagstaff
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  2. Richard Wicklein
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Correspondence to Sean Sather-Wagstaff.

Additional information

Presented by Henning Krause.

Sean Sather-Wagstaff was supported in part by a grant from the NSA

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Sather-Wagstaff, S., Wicklein, R. Extended Local Cohomology and Local Homology. Algebr Represent Theor 19, 1217–1238 (2016). https://doi.org/10.1007/s10468-016-9616-5

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  • DOI: https://doi.org/10.1007/s10468-016-9616-5

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