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

We study t-structures on D(R) the derived category of modules over a commutative Noetherian ring R generated by complexes in . We prove that they are exactly the compactly generated t-structures on D(R) and describe them in terms of decreasing filtrations by supports of 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 immediate generalizations of each point in ϕ(i+1). If a compactly generated t-structure on D(R) restricts to a t-structure on Dfg(R) then the corresponding filtration satisfies the weak Cousin condition. If R has a pointwise dualizing complex the converse is true. If the ring R has dualizing complex then these are exactly all the t-structures on .