Reconstruction from Koszul homology and applications to module and   derived categories
  Let R be a commutative noetherian ring. Let M be a finitely generated R-module. In this paper, we reconstruct M from its Koszul homology with respect to a suitable sequence of elements of R by taking direct summands, syzygies and extensions, and count the number of those operations. Using this result, we consider generation and classification of certain subcategories of the category of finitely generated R-modules, its bounded derived category and the singularity category of R. 
Ryo Takahashi
math.AC math.RT