scholarly journals Symplectic Tate homology

2016 ◽  
Vol 112 (1) ◽  
pp. 169-205 ◽  
Author(s):  
Peter Albers ◽  
Kai Cieliebak ◽  
Urs Frauenfelder
Keyword(s):  
Tate Homology

Tate Homology of Modules Based on Tate $$\mathcal {F}_C$$ F C -Resolutions

2018 ◽  
Vol 44 (2) ◽  
pp. 329-340
Author(s):  
Pengju Ma ◽  
Renyu Zhao ◽  
Xiaoqiang Luo
Keyword(s):  
Tate Homology

Relative and Tate homology with respect to semidualizing modules

2014 ◽  
Vol 13 (08) ◽  
pp. 1450058 ◽  
Author(s):  
Zhenxing Di ◽  
Xiaoxiang Zhang ◽  
Zhongkui Liu ◽  
Jianlong Chen
Keyword(s):  
Exact Sequence ◽  
London Math ◽  
Projective Dimension ◽  
Relative Cohomology ◽  
Relative Homology ◽  
Semidualizing Module ◽  
Coherent Ring ◽  
Semidualizing Modules ◽  
Tate Homology ◽  
Dualizing Module

We introduce and investigate in this paper a kind of Tate homology of modules over a commutative coherent ring based on Tate ℱC-resolutions, where C is a semidualizing module. We show firstly that the class of modules admitting a Tate ℱC-resolution is equal to the class of modules of finite 𝒢(ℱC)-projective dimension. Then an Avramov–Martsinkovsky type exact sequence is constructed to connect such Tate homology functors and relative homology functors. Finally, motivated by the idea of Sather–Wagstaff et al. [Comparison of relative cohomology theories with respect to semidualizing modules, Math. Z. 264 (2010) 571–600], we establish a balance result for such Tate homology over a Cohen–Macaulay ring with a dualizing module by using a good conclusion provided in [E. E. Enochs, S. E. Estrada and A. C. Iacob, Balance with unbounded complexes, Bull. London Math. Soc. 44 (2012) 439–442].

Gorenstein FI-Flat Dimension and Tate Homology

2016 ◽  
Vol 44 (4) ◽  
pp. 679-695 ◽  
Author(s):  
Chelliah Selvaraj ◽  
Vasudevan Biju ◽  
Ramalingam Udhayakumar
Keyword(s):  
Flat Dimension ◽  
Tate Homology

scholarly journals Vanishing of Tate homology and depth formulas over local rings

2015 ◽  
Vol 219 (3) ◽  
pp. 464-481 ◽  
Author(s):  
Lars Winther Christensen ◽  
David A. Jorgensen
Keyword(s):  
Local Rings ◽  
Tate Homology

Complete flat resolutions, Tate homology and the depth formula

2017 ◽  
Vol 40 (1) ◽  
pp. 1-15
Author(s):  
Yanping Liu ◽  
Zhongkui Liu ◽  
Xiaoyan Yang
Keyword(s):  
Tate Homology

Vanishing of Tate homology — An application of stable homology for complexes

2016 ◽  
Vol 32 (7) ◽  
pp. 831-844 ◽  
Author(s):  
Yan Ping Liu ◽  
Zhong Kui Liu ◽  
Xiao Yan Yang
Keyword(s):  
Tate Homology

Gorenstein $$n$$ n -flat dimension and Tate homology

2015 ◽  
Vol 7 (4) ◽  
pp. 309-324
Author(s):  
C. Selvaraj ◽  
R. Udhayakumar
Keyword(s):  
Flat Dimension ◽  
Tate Homology

Tate (Co)homology of invariant group chains

2020 ◽  
pp. 1-23
Author(s):  
Rolando Jimenez ◽  
Angelina López Madrigal
Keyword(s):  
Finite Group ◽  
Abelian Group ◽  
Tate Cohomology ◽  
Invariant Group ◽  
Tate Homology ◽  
A Finite Group ◽  
Group Automorphisms

Let [Formula: see text] be a finite group acting on a group [Formula: see text] as a group automorphisms, [Formula: see text] the bar complex, [Formula: see text] the homology of invariant group chains and [Formula: see text] the cohomology invariant, both defined in Knudson’s paper “The homology of invariant group chains”. In this paper, we define the Tate homology of invariants [Formula: see text] and the Tate cohomology of invariants [Formula: see text]. When the coefficient [Formula: see text] is the abelian group of the integers, we proved that these groups are isomorphics, [Formula: see text]. Further, we prove that the homology and cohomology of invariant group chains are duals, [Formula: see text], [Formula: see text].

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