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Intersections of resolving subcategories and intersections of thick subcategories

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Abstract

Let R be a commutative Noetherian local ring. We consider how nontrivial resolving/thick subcategories of abelian/triangulated categories associated to R intersect. It is understood well when R is a complete intersection or a Cohen–Macaulay ring of finite representation type.

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Notes

  1. This directly follows from [32, Theorem 8.15] in the case where R is a homomorphic image of a regular local ring.

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Acknowledgements

The author thanks Tokuji Araya for giving helpful comments and useful suggestions. The author also thanks the referee for reading the paper carefully and giving valuable comments.

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

    Ryo Takahashi

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  1. Ryo Takahashi
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Correspondence to Ryo Takahashi.

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The author was partly supported by JSPS Grant-in-Aid for Scientific Research 19K03443.

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Takahashi, R. Intersections of resolving subcategories and intersections of thick subcategories. European Journal of Mathematics 7, 1767–1790 (2021). https://doi.org/10.1007/s40879-021-00470-z

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