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

Abstract

We classify compactly generated co-t-structures on the derived category of a commutative noetherian ring. In order to accomplish that, we develop a theory for compactly generated Hom-orthogonal pairs (also known as torsion pairs in the literature) in triangulated categories that resembles Bousfield localization theory. Finally, we show that the category of perfect complexes over a connected commutative noetherian ring admits only the trivial co-t-structures and (de)suspensions of the canonical co-t-structure and use this to describe all silting objects in the category.

34 pages. Version 2: minor corrections, references added and updated

References in corpus (2)

• On exact categories and applications to triangulated adjoints and model structures
• Tilting, cotilting, and spectra of commutative noetherian rings

Cited by in corpus (18)

• Silting objects
• Definability and approximations in triangulated categories
• Smashing localizations of rings of weak global dimension at most one
• $t$-Structures on stable derivators and Grothendieck hearts
• $t$-Structures with Grothendieck hearts via functor categories
• Ladders and simplicity of derived module categories
• On torsion pairs, (well generated) weight structures, adjacent $t$-structures, and related (co)homological functors
• Gorenstein homological algebra and universal coefficient theorems
• On morphisms killing weights, weight complexes, and Eilenberg-Maclane (co)homology of spectra
• Lifting of recollements and gluing of partial silting sets
• From weight structures to (orthogonal) $t$-structures and back
• On constructing weight structures and extending them to idempotent extensions
• Morita theory for stable derivators
• Tilting theory via stable homotopy theory
• Duality pairs, phantom maps, and definability in triangulated categories
• Tilting complexes and codimension functions over commutative noetherian rings
• Generalized periodicity theorems
• Fishing for complements