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arXiv · 1710.10018

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

Arash Sadeghi·Ryo Takahashi
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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.

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Arash Sadeghi, Ryo Takahashi. 2017-10-27. Resolving subcategories closed under certain operations and a conjecture of Dao and Takahashi. https://arxiv.org/abs/1710.10018

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