A remark on the Hochschild-Kostant-Rosenberg theorem in characteristic p

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We prove a Hochschild-Kostant-Rosenberg decomposition theorem for smooth proper schemes X in characteristic p when X≤ p. The best known previous result of this kind, due to Yekutieli, required X<p. Yekutieli's result follows from the observation that the denominators appearing in the classical proof of HKR do not divide p when X<p. Our extension to X=p requires a homological fact: the Hochschild homology of a smooth proper scheme is self-dual.