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