Acyclicity of Tate constructions

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Abstract

We prove that a Tate construction A〈u1,...,un|∂(ui)=zi〉 over a differential graded algebra A, on cycles z1,...,zn in A≥1, is acyclic if and only if the map of graded-commutative algebras H0(A)[y1,...,yn]→H(A), with yi→cls(zi), is an isomorphism. This is used to establish that if a large homomorphism R→S has an acyclic closure R〈U〉 with sup{i|Ui≠Ø}=s<∞, then s is either 1 or an even integer. © 2001 Elsevier Science B.V.

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Iyengar, S. (2001). Acyclicity of Tate constructions. Journal of Pure and Applied Algebra, 163(3), 289–300. https://doi.org/10.1016/S0022-4049(00)00165-1

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