RESEARCH ARTICLE

Complete cohomology for complexes with finite Gorenstein AC-projective dimension

  • Jiangsheng HU 1,2 ,
  • Yuxian GENG , 2 ,
  • Qinghua JIANG 3
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  • 1. School of Mathematics Sciences, Nanjing Normal University, Nanjing 210046, China
  • 2. School of Mathematics and Physics, Jiangsu University of Technology, Changzhou 213001, China
  • 3. School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014, China

Received date: 30 Nov 2015

Accepted date: 04 Feb 2016

Published date: 30 Aug 2016

Copyright

2016 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

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.

Cite this article

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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