Homotopy categories of unbounded complexes of projective modules
Commutative Algebra
2022-03-09 v5
Abstract
We develop in this paper a stable theory for projective complexes, by which we mean to consider a chain complex of finitely generated projective modules as an object of the factor category of the homotopy category modulo split complexes. As a result of the stable theory we are able to prove that a complex of finitely generated projective modules over a generically Gorenstein ring is exact if and only if its dual complex is exact. This shows the dependence of total reflexivity conditions for modules over a generically Gorenstein ring.
Keywords
Cite
@article{arxiv.1805.05705,
title = {Homotopy categories of unbounded complexes of projective modules},
author = {Yuji Yoshino},
journal= {arXiv preprint arXiv:1805.05705},
year = {2022}
}
Comments
Some errors and typos are corrected, and several examples are added