Frontiers of Mathematics in China >
Complete cohomology for complexes with finite Gorenstein AC-projective dimension
Received date: 30 Nov 2015
Accepted date: 04 Feb 2016
Published date: 30 Aug 2016
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We study complete cohomology of complexes with finite Gorenstein AC-projective dimension. We show first that the class of complexes admitting a complete level resolution is exactly the class of complexes with finite Gorenstein AC-projective dimension. This lets us give some general techniques for computing complete cohomology of complexes with finite Gorenstein ACprojective dimension. As a consequence, the classical relative cohomology for modules of finite Gorenstein AC-projective dimension is extended. Finally, the relationships between projective dimension and Gorenstein AC-projective dimension for complexes are given.
Jiangsheng HU , Yuxian GENG , Qinghua JIANG . Complete cohomology for complexes with finite Gorenstein AC-projective dimension[J]. Frontiers of Mathematics in China, 2016 , 11(4) : 901 -920 . DOI: 10.1007/s11464-016-0564-5
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