CLASSIFYING COMPACTLY GENERATED t-STRUCTURES ON THE DERIVED CATEGORY OF A NOETHERIAN RING

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 the set φ(i) contains all the inmediate generalizations of each point in φ(i+ 1). Every t-structure on Dbfg(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 Dbfg(R). More generally, if R has a pointwise dualizing complex we classify all compactly generated t-structures on Dfg(R).