Total Betti numbers of modules of finite projective dimension

• 成果类型: Article
• 署名作者: Walker, Mark E.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2017.186.2.6
• 发表日期: 2017
• 页码: 641-646
• 关键词: adams-operations

摘要

The Buchsbaum-Eisenbud-Horrocks Conjecture predicts that the ith Betti number beta(i)(M) of a nonzero module M of finite length and finite projective dimension over a local ring R of dimension d should be at least ((d)(i)). It would follow from the validity of this conjecture that Sigma(i)beta(i)(M)>= 2d. We prove the latter inequality holds in a large number of cases and that, when R is a complete intersection in which 2 is invertible, equality holds if and only if M is isomorphic to the quotient of R by a regular sequence of elements.