Resolving subcategories closed under certain operations and a conjecture of Dao and Takahashi
Commutative Algebra
2017-10-30 v1 Representation Theory
Abstract
Let R be a commutative Noetherian local ring with residue field k. Let X be a resolving subcategory of finitely generated R-modules. This paper mainly studies when X contains k or consists of totally reflexive modules. It is proved that X does so if X is closed under cosyzygies. A conjecture of Dao and Takahashi is also shown to hold in several cases.
Keywords
Cite
@article{arxiv.1710.10018,
title = {Resolving subcategories closed under certain operations and a conjecture of Dao and Takahashi},
author = {Arash Sadeghi and Ryo Takahashi},
journal= {arXiv preprint arXiv:1710.10018},
year = {2017}
}