论文标题
定义veronese子环的理想的共同体学维度
Cohomological dimension of ideals defining Veronese subrings
论文作者
论文摘要
鉴于在换向的Noetherian环上的标准分级多项式环$ a $，我们证明了定义其任何Veronese子线的理想的共同体学维度和理想的高度相等。当$ a $是特征零字段时，该结果是由于ogus造成的，并且源于佩斯金和szpiro的结果，而当$ a $是一个积极特征的领域时；例如，当$ a $是整数圈时，我们的结果适用。
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.
