Cohomological dimension of ideals defining Veronese subrings

Abstract

Given a standard graded polynomial ring over a commutative Noetherian ring A 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 A is a field of characteristic zero, and follows from a result of Peskine and Szpiro when A A is a field of positive characteristic; our result applies, for example, when A A is the ring of integers.