Classifying Compactly generated t-structures on the derived category of a Noetherian ring

Abstract

We classify complactly generated t-structures on the derived category of modules over a commutative Noetherian ring R in terms of decreasing filtrations by supports on Spec(R). A decreasing filtration by supports ϕ: Z -> Spec(R) satisfies the weak Cousin condition if for any integer i \in Z, the set ϕ(i) contains all the inmediate generalizations of each point in ϕ(i+1). Every t-structure on D^b_fg(R) (equivalently, on D^-_fg(R)) is induced by complactly generated t-structures on D(R) whose associated filtrations by supports satisfy the weak Cousin condition. If the ring R has dualizing complex we prove that these are exactly the t-structures on D^b_fg(R). More generally, if R has a pointwise dualizing complex we classify all compactly generated t-structures on D_fg(R).

v2 41 pages, improved exposition.