Balance with Unbounded Complexes

Edgar E. Enochs; Sergio Estrada; Alina C. Iacob

doi:10.1112/blms/bdr101

Balance with Unbounded Complexes

Edgar E. Enochs, Sergio Estrada, Alina C. Iacob

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

1 Downloads (Pure)

Abstract

Given a double complex X there are spectral sequences with the E2 terms being either HI (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_II(X)=H _II(X)=0. With this result, we give a new and elementary proof of balance of Tate homology and cohomology.

Original language	American English
Journal	Bulletin of the London Mathematical Society
Volume	44
DOIs	https://doi.org/10.1112/blms/bdr101
State	Published - Jun 2012

Keywords

Unbound complexes

DC Disciplines

Mathematics

Access to Document

10.1112/blms/bdr101License: Unspecified

fulltext.pdfFinal published version, 82 KBLicense: Unspecified

Cite this

@article{e358a3767b1a4429817ec91e2ba149f1,

title = "Balance with Unbounded Complexes",

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 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 HII(X)=H II(X)=0. With this result, we give a new and elementary proof of balance of Tate homology and cohomology.",

keywords = "Unbound complexes",

author = "Enochs, {Edgar E.} and Sergio Estrada and Iacob, {Alina C.}",

note = "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",

year = "2012",

month = jun,

doi = "10.1112/blms/bdr101",

language = "American English",

volume = "44",

journal = "Bulletin of the London Mathematical Society",

issn = "0024-6093",

publisher = "John Wiley and Sons Ltd",

}

TY - JOUR

T1 - Balance with Unbounded Complexes

AU - Enochs, Edgar E.

AU - Estrada, Sergio

AU - Iacob, Alina C.

N1 - 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

PY - 2012/6

Y1 - 2012/6

N2 - 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 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 HII(X)=H II(X)=0. With this result, we give a new and elementary proof of balance of Tate homology and cohomology.

AB - 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 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 HII(X)=H II(X)=0. With this result, we give a new and elementary proof of balance of Tate homology and cohomology.

KW - Unbound complexes

U2 - 10.1112/blms/bdr101

DO - 10.1112/blms/bdr101

M3 - Article

SN - 0024-6093

VL - 44

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

ER -

Balance with Unbounded Complexes

Abstract

Keywords

DC Disciplines

Access to Document

Fingerprint

Cite this