Singularity categories and singular equivalences for resolving subcategories
Abstract
Let X be a resolving subcategory of an abelian category. In this paper we investigate the singularity category Dsg(X−−)=Db(modX−−)/Kb(proj(modX−−)) of the stable category X−− of X. We consider when the singularity category is triangle equivalent to the stable category of Gorenstein projective objects, and when the stable categories of two resolving subcategories have triangle equivalent singularity categories. Applying this to the module category of a Gorenstein ring, we prove that the complete intersections over which the stable categories of resolving subcategories have trivial singularity categories are the simple hypersurface singularities of type (A1). We also generalize several results of Yoshino on totally reflexive modules.
Journal
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- Mathematische Zeitschrift
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Mathematische Zeitschrift 285 (1), 251-286, 2017-02
Springer
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Keywords
Details 詳細情報について
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- CRID
- 1050282813782452864
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- NII Article ID
- 120006024328
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- ISSN
- 14321823
- 00255874
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- HANDLE
- 2237/25977
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- Text Lang
- en
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- Article Type
- journal article
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- Data Source
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- IRDB
- Crossref
- CiNii Articles
- KAKEN