2016/02/10 by Sean Sather-Wagstaff, Sather-Wagstaff, Sean, Richard Wicklein +1 · 3 citations
Mathematics · #13B35 #13C12 #13D09 #13D45 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AC #msc:13B35 #msc:13C12 #msc:13D09 #msc:13D45
paper · pdf · doi:10.48550/arxiv.1602.03226
21 pages. part 4 of a series with arXiv:1401.6925, arXiv:1506.07052, arXiv:1602.03224, arXiv:1602.03225, and arXiv:1602.03227. comments welcome. v.2 adds references to work of Shaul (which include Theorem 1.2 from v.1), updates other references, and updates URL for Sather-Wagstaff
openalex publication_date 2016/02/10 · arxiv created 2016/02/23 · arxiv updated 2016/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present an in-depth exploration of the module structures of local (co)homology modules (moreover, for complexes) over the completion \widehat R\mathfrak a of a commutative noetherian ring R with respect to a proper ideal \mathfrak a. In particular, we extend Greenlees-May Duality and MGM Equivalence to track behavior over \widehat R\mathfrak 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.