Hearts for commutative noetherian rings: derived equivalences and torsion pairs

Abstract: The structure of the category of modules over a commutative noetherian ring R and of its derived category is largely controlled by the prime spectrum of R. In this talk we discuss how this control extends to the structure of hearts of t-structures in the derived category. We will focus in particular on hearts arising from hereditary torsion pairs in Mod(R). These turn out to be Grothendieck categories which are derived equivalent to R and such that part of the lattice of torsion pairs can be studied using the prime spectrum of R. This talk is based on joint work with Sergio Pavon.

Mathematics

Audience: researchers in the topic

Aarhus Homological Algebra Seminar