Acyclicity of Tate constructions

We prove that a Tate construction Aleft angle bracketu1,…,un ∂(ui)=ziright-pointing angle bracket 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 yimaps tocls(zi), is an isomorphism. This is used to establish that if a large homomorphism R→S has an acyclic closure Rleft angle bracketUright-pointing angle bracket with sup{i Ui≠empty set︀}=s<∞, then s is either 1 or an even integer.