Hearts for commutative noetherian rings: torsion pairs and derived equivalences

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).