Resolving subcategories whose finitely presented module categories are abelian

Ryo Takahashi

doi:10.5802/crmath.197

Algèbre, Théorie des représentations

Resolving subcategories whose finitely presented module categories are abelian

Ryo Takahashi ¹

¹ Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya 464-8602, Japan

Comptes Rendus. Mathématique, Volume 359 (2021) no. 5, pp. 577-592.

Résumé

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 $\mod 𝒳$ 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.

Reçu le : 2021-01-27
Révisé le : 2021-03-18
Accepté le : 2021-03-18
Publié le : 2021-07-13

DOI : 10.5802/crmath.197

Classification : 13C60, 18A25, 18E10

Affiliations des auteurs :

Ryo Takahashi ¹

¹ Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya 464-8602, Japan

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Ryo Takahashi},
     title = {Resolving subcategories whose finitely presented module categories are abelian},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {577--592},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {5},
     year = {2021},
     doi = {10.5802/crmath.197},
     language = {en},
}

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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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