On compactly generated torsion pairs and the classification of co-$t$-structures for commutative noetherian rings

DOI10.1090/tran/6561zbMath1346.18018arXiv1212.3122OpenAlexW1679926428WikidataQ105335870 ScholiaQ105335870MaRDI QIDQ2790732

Jan Šťovíček, David Pospíšil

Publication date: 8 March 2016

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.3122

zbMATH Keywords

commutative Noetherian ringco-t-structurestable derivatorcompactly generated Hom-orthogonal pair

Mathematics Subject Classification ID

Structure, classification theorems for modules and ideals in commutative rings (13C05) Differential graded algebras and applications (associative algebraic aspects) (16E45)

Related Items

Smashing localizations of rings of weak global dimension at most one, Compactly generated t-structures in the derived category of a commutative ring, Gorenstein homological algebra and universal coefficient theorems, \(t\)-structures with Grothendieck hearts via functor categories, Tensor weight structures and \(t\)-structures on the derived categories of schemes, Killing weights from the perspective of \(t\)-structures, \(t\)-structures on stable derivators and Grothendieck hearts, Silting and cosilting classes in derived categories, Compactly generated tensor t-structures on the derived categories of Noetherian schemes, Stratifying derived module categories, Tilting theory via stable homotopy theory, On torsion theories, weight and \(t\)-structures in triangulated categories, A Nullstellensatz for triangulated categories, On perfectly generated weight structures and adjacent \(t\)-structures, Silting Objects, On infinite effectivity of motivic spectra and the vanishing of their motives, Parametrizing torsion pairs in derived categories, Lifting of recollements and gluing of partial silting sets

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Auslander-Buchweitz context and co-\(t\)-structures
• On exact categories and applications to triangulated adjoints and model structures
• Mayer-Vietoris sequences in stable derivators
• The localization of spectra with respect to homology
• Compactly generated \(t\)-structures on the derived category of a noetherian ring
• Equivariant stable homotopy theory. With contributions by J. E. McClure
• The chromatic tower for \(D(R)\). With an appendix by Marcel Bökstedt
• A remark on the generalized smashing conjecture
• Chain complexes and stable categories
• Cotorsion pairs, model category structures, and representation theory
• Cohomological direct images in model categories
• Derivators, pointed derivators and stable derivators
• The telescope conjecture for hereditary rings via Ext-orthogonal pairs.
• Relative homological algebra and purity in triangulated categories
• Compact corigid objects in triangulated categories and co-\(t\)-structures
• A DG guide to Voevodsky's motives
• Silting objects, simple-minded collections, \(t\)-structures and co-\(t\)-structures for finite-dimensional algebras.
• Models for singularity categories.
• Additivity for derivator \(K\)-theory
• Mutation in triangulated categories and rigid Cohen-Macaulay modules
• Approximations and endomorphism algebras of modules.
• t-structures and cotilting modules over commutative Noetherian rings
• Les foncteurs dérivés de lim et leurs applications en théorie des modules
• Exact categories
• Triangulated Categories
• A Note on Compactly Generated Co-t-Structures
• Silting mutation in triangulated categories
• Generalized tensor idempotents and the telescope conjecture
• Localization theory for triangulated categories
• Weight structures vs.t-structures; weight filtrations, spectral sequences, and complexes (for motives and in general)
• Derived categories and universal problems
• ENHANCED TRIANGULATED CATEGORIES
• REPRESENTABLE FUNCTORS, SERRE FUNCTORS, AND MUTATIONS
• Localization with Respect to Certain Periodic Homology Theories
• Morita Theory for Derived Categories
• Homotopy theories
• Deriving DG categories
• Axiomatic stable homotopy theory
• THE CO-STABILITY MANIFOLD OF A TRIANGULATED CATEGORY
• Deconstructibility and the Hill Lemma in Grothendieck categories
• Weight Structures and Simple dg Modules for Positive dg Algebras
• The connection between the $K$-theory localization theorem of Thomason, Trobaugh and Yao and the smashing subcategories of Bousfield and Ravenel
• Tilting, cotilting, and spectra of commutative noetherian rings
• Homological and homotopical aspects of torsion theories
• On \(t\)-structures and torsion theories induced by compact objects