Algebra, Representation theory
Resolving subcategories whose finitely presented module categories are abelian
Comptes Rendus. Mathématique, Volume 359 (2021) no. 5, pp. 577-592.

Let $𝒳$ be an additive full subcategory of an abelian category. It is a classical fact that if $𝒳$ is contravariantly finite, then the category $\mathsf{mod}\phantom{\rule{0.166667em}{0ex}}𝒳$ of finitely presented right $𝒳$-modules is abelian. In this paper, we consider the question asking when the converse holds true for a resolving subcategory of the category of finitely generated modules over a commutative noetherian henselian local ring. We give both affirmative answers and negative answers to this question.

Revised:
Accepted:
Published online:
DOI: https://doi.org/10.5802/crmath.197
Classification: 13C60,  18A25,  18E10
Ryo Takahashi 1

1. Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya 464-8602, Japan
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Ryo Takahashi. Resolving subcategories whose finitely presented module categories are abelian. Comptes Rendus. Mathématique, Volume 359 (2021) no. 5, pp. 577-592. doi : 10.5802/crmath.197. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.197/

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