Hearts for commutative noetherian rings: torsion pairs and derived equivalences

Abstract

Over a commutative noetherian ring $R$, the prime spectrum controls, via the assignment of support, the structure of both $\mathsf{Mod}(R)$ and $\mathsf{D}(R)$. We show that, just like in $\mathsf{Mod}(R)$, the assignment of support classifies hereditary torsion pairs in the heart of any nondegenerate compactly generated $t$-structure of $\mathsf{D}(R)$. Moreover, we investigate whether these $t$-structures induce derived equivalences, obtaining a new source of Grothendieck categories which are derived equivalent to $\mathsf{Mod}(R)$.

arXiv comment24 pages, comments are welcome! Version 2 contains some minor changes and clarifications

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Cited by in corpus (5)

• Tilting complexes and codimension functions over commutative noetherian rings
• Mutation and torsion pairs
• Torsion-simple objects in abelian categories
• Singular equivalences to locally coherent hearts of commutative noetherian rings
• Mutation and the Gabriel spectrum