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In what generality of commutative associative algebras does there exist a minimal Koszul-Tate resolution? Or what is the most general condition known?

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By minimal K-T resolution you mean a CDGA which as an algebra $\mathcal A$ is a polynomial algebra on a nonnegatively graded vector space and whose differential lands in $\mathcal A^+\cdot\mathcal A^+$ q-iso to your initial algebra $A$? –  Mariano Suárez-Alvarez Jul 23 '13 at 6:32

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