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 \phi : Z -> Spec(R) satisfies the weak Cousin condition if for any integer i \in Z, the set \phi(i) contains all the inmediate generalizations of each point in \phi(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).
Cite
@article{arxiv.0706.0499,
title = {Classifying Compactly generated t-structures on the derived category of a Noetherian ring},
author = {Leovigildo Alonso and Ana Jeremias and Manuel Saorin},
journal= {arXiv preprint arXiv:0706.0499},
year = {2017}
}