In the 1960s, Grothendieck introduced the notion of local cohomology from the viewpoint of
geometry. It has brought great benefits to commutative algebra, and has been an essential …

Given a cohomological functor from a triangulated category to an abelian category, we
construct under appropriate assumptions for any localization functor of the abelian category …

LOCALIZATION FUNCTORS IN DERIVED CATEGORIES OF COMMUTATIVE
NOETHERIAN RINGS 1. Introduction This article is based on joint work Page 1 …

Bousfield localization is a technique that has been used extensively in algebraic topology,
specifically in stable homotopy theory, over the last quarter century. Its name derives from …

Let $ A $ be a commutative noetherian ring. In this paper, we interpret localizing
subcategories of the derived category of $ A $ by using subsets of Spec $ A $ and …

arXiv:1012.1540v2 [math.AT] 4 Jan 2011 Page 1 arXiv:1012.1540v2 [math.AT] 4 Jan 2011 A
CHARACTERIZATION OF SIMPLICIAL LOCALIZATION FUNCTORS C. BARWICK AND DM …

Let R be a commutative Noetherian ring. We introduce the notion of colocalization functors γ
W with supports in arbitrary subsets W of Spec R. If W is a specialization-closed subset, then …

We prove a new localization theorem for algebraic stable categories when the localizing
subcategory is generated by a precovering class in the model category. We use this to show …

Let b be a Waldhausen category, alias category with cofibrations and weak equivalences.
The hammock localization (Dwyer and Kan, 1980) of b with respect to the subcategory cof …

Rings and modules of quotients with respect to an additive topology F or a localizing
subcategory of R y Mod were introduced by Gabriel in his wx thesis 3, and have been an …