Reconstruction from Koszul homology and applications to module and derived categories
Commutative Algebra
2016-01-20 v2 Representation Theory
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.
Keywords
Cite
@article{arxiv.1210.1982,
title = {Reconstruction from Koszul homology and applications to module and derived categories},
author = {Ryo Takahashi},
journal= {arXiv preprint arXiv:1210.1982},
year = {2016}
}
Comments
14 pages, final version, to appear in Pacific J. Math