Support and adic finiteness for complexes

DOI10.1080/00927872.2015.1087008zbMath1386.13046arXiv1401.6925OpenAlexW2964159921MaRDI QIDQ5274852

Richard Wicklein, Sean K. Sather-Wagstaff

Publication date: 6 July 2017

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.6925

zbMATH Keywords

derived categoriesKoszul homologylocal cohomologylocal homologycofinite complexesadically finite complexes

Mathematics Subject Classification ID

Syzygies, resolutions, complexes and commutative rings (13D02) Local cohomology and commutative rings (13D45) Completion of commutative rings (13B35) Complete rings, completion (13J10) Derived categories and commutative rings (13D09)

Related Items (22)

Local homology, Koszul homology and Serre classes ⋮ Filter depth of complexes ⋮ Adic semidualizing complexes ⋮ Extended local cohomology and local homology ⋮ Cosupport computations for finitely generated modules over commutative noetherian rings ⋮ Adic reduction to the diagonal and a relation between cofiniteness and derived completion ⋮ Adically finite chain complexes ⋮ Local homology, finiteness of Tor modules and cofiniteness ⋮ COSUPPORT FOR COMPACTLY GENERATED TRIANGULATED CATEGORIES ⋮ Minimal semi-flat-cotorsion replacements and cosupport ⋮ Sequence-regular commutative DG-rings ⋮ Unnamed Item ⋮ Stable under specialization sets and cofiniteness ⋮ A new outlook on cofiniteness ⋮ Adic Foxby classes ⋮ Gorenstein injective filtrations over Cohen-Macaulay rings with dualizing modules ⋮ Relative tensor triangular Chow groups for coherent algebras ⋮ Localization functors and cosupport in derived categories of commutative Noetherian rings ⋮ Complete intersection Hom injective dimension ⋮ Adic finiteness: Bounding homology and applications ⋮ Cosupports and minimal pure-injective resolutions of affine rings ⋮ Using semidualizing complexes to detect Gorenstein rings

Cites Work

• Unnamed Item
• Unnamed Item
• Extended local cohomology and local homology
• On a characterization of cofinite complexes. Addendum to ``On a category of cofinite modules which is abelian
• On a category of cofinite modules which is abelian
• Homological dimensions of unbounded complexes
• Derived functors of \(I\)-adic completion and local homology
• Bounded complexes of flat modules
• Cofinite modules and local cohomology
• Vanishing of local homology
• Tensor product of dualizing complexes over a field
• Modules cofinite with respect to an ideal
• On the homology of completion and torsion
• Homology of artinian and mini-max module. II
• Support and injective resolutions of complexes over commutative rings
• Liftings and quasi-liftings of DG modules
• Local cohomology. A seminar given by A. Grothendieck, Harvard University, Fall 1961. Notes by R. Hartshorne
• Affine duality and cofiniteness
• Residues and duality. Lecture notes of a seminar on the work of A. Grothendieck, given at Havard 1963/64. Appendix: Cohomology with supports and the construction of the \(f^!\) functor by P. Deligne
• Complete modules and torsion modules
• On invariants dual to the Bass numbers
• Locally Gorenstein Homomorphisms
• Local homology and cohomology on schemes
• DUALIZING DIFFERENTIAL GRADED MODULES AND GORENSTEIN DIFFERENTIAL GRADED ALGEBRAS
• Cohomologically Cofinite Complexes
• A Separated Cohomologically Complete Module is Complete
• A Somewhat Gentle Introduction to Differential Graded Commutative Algebra

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