On the acyclicity of the Tate complex Original Research Article

We give a characterization of the acyclicity of the second step of a Tate or simplicial resolution of a commutative algebra. As a consequence, we obtain a characterization of the vanishing of André-Quillen cohomology of a surjectivc homomorphism ø:A → B, H1(A, B,−) = 0 for all j ≥ 3, in terms of the Koszul homology of Ker(ø).