Complete cohomology for complexes with finite Gorenstein AC-projective dimension

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.

Keywords

Gorenstein AC-projective / complete level resolution / complete cohomology

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2016 Higher Education Press and Springer-Verlag Berlin Heidelberg