no. 5
Algèbre, Théorie des représentations
Resolving subcategories whose finitely presented module categories are abelian
Takahashi, Ryo1
1 Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya 464-8602, Japan
Comptes Rendus. Mathématique, Tome 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 mod𝒳 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.

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DOI : 10.5802/crmath.197
Classification : 13C60, 18A25, 18E10
Takahashi, Ryo 1

1 Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya 464-8602, Japan 
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Takahashi, Ryo. Resolving subcategories whose finitely presented module categories are abelian. Comptes Rendus. Mathématique, Tome 359 (2021) no. 5, pp. 577-592. doi : 10.5802/crmath.197. http://www.numdam.org/articles/10.5802/crmath.197/

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