  We investigate the relationship between smoothness and the relative global
dimension. We prove that a smooth ring map $B\to A$ between commutative rings
implies the finiteness of the relative global dimension
$\operatorname{gldim}(A,B)$. Conversely, we identify a sufficient condition on
$B$ such that the finiteness of $\operatorname{gldim}(A,B)$ implies the
smoothness of the map $B\to A$.
