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

Cohomological dimension of ideals defining Veronese subrings