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Classifying resolving subcategories over a Cohen–Macaulay local ring

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Abstract

Let R be a Cohen–Macaulay local ring. Denote by mod R the category of finitely generated R-modules. In this paper, we consider the classification problem of resolving subcategories of mod R in terms of specialization-closed subsets of Spec R. We give a classification of the resolving subcategories closed under tensor products and transposes. Under restrictive hypotheses, we also give better classification results.

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Author notes

  1. Ryo Takahashi

    Present address: Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya, 464-8602, Japan

Authors and Affiliations

  1. Department of Mathematical Sciences, Faculty of Science, Shinshu University, 3-1-1 Asahi, Matsumoto, Nagano, 390-8621, Japan

    Ryo Takahashi

  2. Department of Mathematics, University of Nebraska, Lincoln, NE, 68588-0130, USA

    Ryo Takahashi

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  1. Ryo Takahashi
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Correspondence to Ryo Takahashi.

Additional information

The author was partially supported by JSPS Grant-in-Aid for Young Scientists (B) 22740008 and by JSPS Postdoctoral Fellowships for Research Abroad.

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Takahashi, R. Classifying resolving subcategories over a Cohen–Macaulay local ring. Math. Z. 273, 569–587 (2013). https://doi.org/10.1007/s00209-012-1020-1

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  • DOI: https://doi.org/10.1007/s00209-012-1020-1

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