Article
Balance with Unbounded Complexes
Bulletin of the London Mathematical Society
(2012)
Abstract
Given a double complex X there are spectral sequences with the E2 terms being either HI (HII(X)) or HII(HI(X)). But if HI(X)=HII(X)=0, then both spectral sequences have all their terms 0. This can happen even though there is nonzero (co)homology of interest associated withX. 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 HI(X)=HII(X)=0. With this result, we give a new and elementary proof of balance of Tate homology and cohomology.
Keywords
- Unbound complexes
Disciplines
Publication Date
June, 2012
DOI
10.1112/blms/bdr101
Publisher Statement
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Citation Information
Edgar E. Enochs, Sergio Estrada, and Alina Iacob. "Balance with Unbounded Complexes" Bulletin of the London Mathematical Society 44.3 (2012): 439-442.doi:10.1112/blms/bdr101
source:http://arxiv.org/abs/1108.1100
Available at: http://works.bepress.com/alina_iacob/23