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arXiv 2005.032502020-05-07math.AC

Cohomological dimension of ideals defining Veronese subrings

Vaibhav Pandey

备注：: 7 pages
发表信息：: Proceedings of the American Mathematical Society, 2021
DOI：: 10.1090/proc/15273

英文摘要：

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.

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