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arXiv · 1707.02678

Tate-Vogel and relative cohomologies of complexes with respect to cotorsion pairs

Jiangsheng Hu·Huanhuan Li·Jiaqun Wei·Xiaoyan Yang·Nanqing Ding
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Abstract

We study Tate-Vogel and relative cohomologies of complexes by applying the model structure induced by a complete hereditary cotorsion pair ($\A$, $\B$) of modules. We show first that the class of complexes admitting a complete $\A$ resolution is exactly the class of complexes with finite Gorenstein $\A$ dimension. This lets us give general techniques for computing Tate-Vogel cohomoloies of complexes with finite Gorenstein $\A$ dimension. As a consequence, relative cohomology groups for complexes with finite Gorenstein $\A$ dimension are investigated. Finally, the relationships between Gorenstein $\A$ dimensions and $\A$ dimensions for complexes are given.

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Jiangsheng Hu, Huanhuan Li, Jiaqun Wei, Xiaoyan Yang, Nanqing Ding. 2017-07-10. Tate-Vogel and relative cohomologies of complexes with respect to cotorsion pairs. https://arxiv.org/abs/1707.02678

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