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      Balance with Unbounded Complexes

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          Abstract

          Given a double complex \(X\) there are spectral sequences with the \(E_2\) terms being either H\(_I\) (H\(_{II}(X))\) or H\(_{II}(\)H\(_I (X))\). But if \(H_I(X)=H_{II}(X)=0\) both spectral sequences have all their terms 0. This can happen even though there is nonzero (co)homology of interest associated with \(X\). This is frequently the case when dealing with Tate (co)homology. So in this situation the spectral sequences may not give any information about the (co)homology of interest. In this article we give a different way of constructing homology groups of \(X\) when H\(_I(X)=\)H\(_{II}(X)=0\). With this result we give a new and elementary proof of balance of Tate homology and cohomology.

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          Absolute Gorenstein and Tate Torsion Modules

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            Balance in Generalized Tate Cohomology

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              Author and article information

              Journal
              04 August 2011
              Article
              10.1112/blms/bdr101
              1108.1100
              569722ac-98c0-46ae-a854-669d84714ec0

              http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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              Custom metadata
              55U15, 16E05, 16E30, 18G15
              math.AC

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