Iterated HRS-tilting and derived equivalences for commutative notherian rings ===== Let R be a commutative noetherian ring. It is well known that the assignment of support allows one to characterise many subcategories of Mod(R) and D(R) in terms of certain subsets of Spec(R): hereditary torsion classes in Mod(R) (see eg [4]), localising (and smashing) subcategories of D(R) ([3]) and, more generally, compactly generated t-structures of D(R) ([1]). In this talk we will see that also in the heart of any (nondegenerate) compactly generated t-structure of D(R), hereditary torsion pairs are classified by support. This fact can be used to show that if two compactly generated t-structures have finite distance from each other, then they are linked by a chain of HRS-tilting procedures, with respect to hereditary torsion pairs of finite type at each step. We will also address the question of whether these HRS-tilts provide derived equivalences, using a criterion from [2]. We will see that if R is a commutative noetherian ring, every hereditary torsion pair in Mod(R) provides derived equivalence; and that if an intermediate (nondegenerate) compactly generated t-structure satisfies some conditions (i.e. it is restrictable, [1]) then the iterated HRS-tilting procedure found above provides a derived equivalence at each step. This talk is based on an ongoing joint work with J. VitÃ³ria. References: [1] Alonso Tarrio, Jeremias Lopez, Saorin. ``Compactly generated t-structures on the derived category of a noetherian ring'', J. Algebra 324, 313-346 [2] Chen, Han, Zhou. ``Derived equivalences via HRS-tilts'', Adv. Math. 345 (2019) [3] Neeman. ``The chromatic tower for D(R)'', Topology 31 (1992), no. 3, 519-532 [4] StenstrÃ¶m. ``Rings of quotients'', Springer-Verlag 1975