Srikanth Iyengar, Henning Krause

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Srikanth Iyengar, Henning Krause

机译：Srikanth Iyengar，Henning Krause

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It is proved that for a commutative noetherian ring with dualizing complex the homotopy category of projective modules is equivalent, as a triangulated category, to the homotopy category of injective modules. Restricted to compact objects, this statement is a reinterpretation of Grothendieck's duality theorem. Using this equivalence it is proved that the (Verdier) quotient of the category of acyclic complexes of projectives by its subcategory of totally acyclic complexes and the corresponding category consisting of injective modules are equivalent. A new characterization is provided for complexes in Auslander categories and in Bass categories of such rings.

机译：证明了，对于具有二元复数的可交换Noether环，射影模块的同伦范畴作为三角范畴与射影模块的同伦范畴相等。限于紧凑对象，此陈述是格洛腾迪克对偶定理的重新解释。利用这种等价关系证明，射影的非环状复合物类别的（Verdier）商是完全非环状复合物的子类别，与相应的由内射模块组成的类别是等价的。为此类环的Auslander类别和Bass类别的复合物提供了新的表征。

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《DOCUMENTA MATHEMATICA》 |2006年第19期|共34页
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中图分类各科教学法、教学参考书;
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1. Thick subcategories of modules over commutative noetherian rings (with an appendix by Srikanth Iyengar) [J] . Henning Krause Mathematische Annalen . 2008,第4期

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Srikanth Iyengar, Henning Krause

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