Duality for cochain DG algebras  

作　　者：JφRGENSEN Peter 

机构地区：[1]School of Mathematics and Statistics,Newcastle University

出　　处：《Science China Mathematics》2013年第1期79-89,共11页中国科学：数学（英文版）

摘　　要：This paper develops a duality theory for connected cochain DG algebras,with particular emphasis on the non-commutative aspects.One of the main items is a dualizing DG module which induces a duality between the derived categories of DG left-modules and DG right-modules with finitely generated cohomology.As an application,it is proved that if the canonical module k=A/A≥1 has a semi-free resolution where the cohomological degree of the generators is bounded above,then the same is true for each DG module with finitely generated cohomology.This paper develops a duality theory for connected cochain DG algebras, with particular emphasis on the non-commutative aspects. One of the main items is a dualizing DG module which induces a duality between the derived categories of DG left-modules and DG right-modules with finitely generated cohomology. As an application, it is proved that if the canonical module k = A/A≥1 has a semi-free resolution where the cohomological degree of the generators is bounded above, then the same is true for each DG module with finitely generated cohomology.

关 键 词：balanced dualizing complex Castelnuovo-Mumford regularity Cech DG module derived comple-tion derived torsion DG left-module DG right-module dualizing DG module endomorphism DG algebra Extregularity non-commutative DG algebra 

分 类 号：O153[理学—数学]