Over a commutative noetherian ring R, the prime spectrum controls, via the assignment of support, the structure of both Mod(R) and D(R). We show that, just like in Mod(R), the assignment of support classifies hereditary torsion pairs in the heart of any nondegenerate compactly generated t-structure of D(R). Moreover, we investigate whether these t-structures induce derived equivalences, obtaining a new source of Grothendieck categories which are derived equivalent to Mod(R).
Over a commutative noetherian ring R, the prime spectrum controls, via the assignment of support, the structure of both Mod(R) and D(R). We show that, just like in Mod(R), the assignment of support classifies hereditary torsion pairs in the heart of any nondegenerate compactly generated t-structure of D(R). Moreover, we investigate whether these t-structures induce derived equivalences, obtaining a new source of Grothendieck categories which are derived equivalent to Mod(R).
Tilting modules, generalising the notion of progenerator, furnish equivalences between pieces of module categories. This paper is dedicated to study how much these pieces say about the whole category. We will survey the existing results in the literature, introducing also some new insights.
We show that Krause's recollement exists for any locally coherent Grothendieck category such that its derived category is compactly generated. As a source of such categories, we consider the hearts of intermediate and restrictable t-structures in the derived category of a commutative noetherian ring. We show that the induced tilting objects in these hearts give rise to an equivalence between the two Krause's recollements, and in particular to a singular equivalence.
ContentsIntroduction 1 1. Preliminaries 2 2. Krause's recollement for locally coherent Grothendieck categories 8 3. Restrictable t-structures 14 4. The equivalence of recollements 17 References 21
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations鈥揷itations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.