A local-global principle for small triangulated categories

Abstract

Local cohomology functors are constructed for the category of cohomological functors on an essentially small triangulated category T equipped with an action of a commutative noetherian ring. This is used to establish a local-global principle and to develop a notion of stratification, for T and the cohomological functors on it, analogous to such concepts for compactly generated triangulated categories.

24 pages. Final version. Accepted for publication with the Mathematical Proceedings of the Cambridge Philosophical Society

References in corpus (2)

• Stratifying triangulated categories
• On the derived category of a graded commutative noetherian ring

Cited by in corpus (6)

• Local duality for representations of finite group schemes
• Affine weakly regular tensor triangulated categories
• Annihilators and dimensions of the singularity category
• Exceptional complete intersection maps of local rings
• Central support for triangulated categories
• A partial converse ghost lemma for the derived category of a commutative noetherian ring