Abstract
We prove converses of the Hochschild-Kostant-Rosenberg Theorem, in particular: If a commutative algebra S is flat and essentially of finite type over a noetherian ring \(\mathbb{k}\), and the Hochschild homology HH*(S|\(\mathbb{k}\)) is a finitely generated S-algebra for shuffle products, then S is smooth over \(\mathbb{k}\).
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