Resolving subcategories closed under certain operations and a conjecture of Dao and Takahashi

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.