A Remark on Vanishing of Chain Complexes

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• 作者：Yuji Yoshino
• 关键词：Commutative noetherian rings ; Derived categories ; Primary 13D09 ; Secondary 13D02
• 刊名：Acta Mathematica Vietnamica
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：40
• 期：1
• 页码：173-177
• 全文大小：143 KB
• 参考文献：1. Benson, DJ, Iyengar, SB, Krause, H (2012) Colocalizing subcategories and cosupport. J. Reine Angew. Math. 673: pp. 161-207
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  4. Foxby, H-B (1979) Bounded complexes of flat modules. J. Pure Appl. Algebra 15: pp. 149-172 CrossRef
  5. Foxby, H.-B., Iyengar, S.B.: Depth and amplitude for unbounded complexes. Commutative algebra (Grenoble/Lyon, 2001), 119-37, Contemp. Math., 331, Am. Math. Soc., Providence, RI (2003)
  6. Neeman, A (1992) The chromatic tower for D(R). Topology 31: pp. 519-532 CrossRef
  7. Neeman, A (2011) Colocalizing subcategories of D(R). J. Reine Angew. Math. 653: pp. 221-243
  
• 刊物主题：Mathematics, general;
• 出版者：Springer Singapore
• ISSN：2315-4144

文摘

For chain complexes \(W \in D^{\pm }_{fg} (R)\) and X ?D(R) in the derived category over a commutative noetherian ring R, we prove that RHom R (W, X) = 0 if and only if W L⊿sub class="a-plus-plus"> R X = 0.