Abstract
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, H 1( A, B,−) = 0 for all j ≥ 3, in terms of the Koszul homology of Ker(ø).
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