Suppose that $A$ is a commutative dgalgebra (say over base $k$) which is bounded in nonpositive degree (with cochain complex conventions). There exists a quasifree resolution of $A$. My question is, under what conditions on $A$ does $A$ admit a quasifree resolution which is also finitely generated (as a graded commutative algebra). Can we completely characterize such algebras intrinsically?
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