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

We prove a Hochschild-Kostant-Rosenberg decomposition theorem for smoothly compactiable smooth schemes X in characteristic p when dimX 6 p. The best known previous result of this kind, due to Yekutieli, required dimX < p. Yekutieli's result follows from the observation that the denominators appearing in the classical proof of HKR do not divide p when dimX < p. Our extension to dimX = p requires a homological fact: the Hochschild homology of a smooth proper scheme is self-dual.