Reconstruction from Koszul homology and applications to module and derived categories

Abstract

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.

14 pages, final version, to appear in Pacific J. Math

References in corpus (4)

• Matrix factorizations for nonaffine LG-models
• Subcategories of singularity categories via tensor actions
• Orlov spectra: bounds and gaps
• A note on thick subcategories of stable derived categories