Singularity Categories, Schur Functors and Triangular Matrix Rings

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• 作者：Xiao-Wu Chen (1)
  
• 关键词：Singularity category ; Schur functor ; Triangular matrix ring ; Gorenstein ring ; 18E30 ; 18E35 ; 16E65
• 刊名：Algebras and Representation Theory
• 出版年：2009
• 出版时间：October 2009
• 年：2009
• 卷：12
• 期：2-5
• 页码：181-191
• 全文大小：361KB
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  15. Orlov, D.: Triangulated categories of singularities and equivalences between Landau鈥揋inzburg models. Mat. Sb. 197, 1827鈥?840 (2006). Also see: math.AG/0503630 CrossRef
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• 作者单位：Xiao-Wu Chen (1)
  
  1. Department of Mathematics, University of Science and Technology of China, Hefei, 230026, People鈥檚 Republic of China
  
• ISSN：1572-9079

文摘

We study certain Schur functors which preserve singularity categories of rings and we apply them to study the singularity category of triangular matrix rings. In particular, combining these results with Buchweitz鈥揌appel鈥檚 theorem, we can describe singularity categories of certain non-Gorenstein rings via the stable category of maximal Cohen鈥揗acaulay modules. Three concrete examples of finite-dimensional algebras with the same singularity category are discussed.