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Balance with unbounded complexes (2012)

Enochs, E. E., Estrada, S., Iacob, A. C.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2012-05-22

Description: 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, then 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.

Print ISSN: 0024-6093

Electronic ISSN: 1469-2120

Topics: Mathematics

Published by Oxford University Press

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