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 $\mathsf{Mod}(R)$.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2020
- DOI:
- 10.48550/arXiv.2009.08763
- arXiv:
- arXiv:2009.08763
- Bibcode:
- 2020arXiv200908763P
- Keywords:
-
- Mathematics - Representation Theory;
- Mathematics - Commutative Algebra;
- Mathematics - Category Theory;
- 13D30;
- 13D09;
- 18E10;
- 18G80
- E-Print:
- 24 pages, comments are welcome! Version 2 contains some minor changes and clarifications