  Given a standard graded polynomial ring over a commutative Noetherian ring
$A$, we prove that the cohomological dimension and the height of the ideals
defining any of its Veronese subrings are equal. This result is due to Ogus
when $A$ is a field of characteristic zero, and follows from a result of
Peskine and Szpiro when $A$ is a field of positive characteristic; our result
applies, for example, when $A$ is the ring of integers.
