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arXiv · 1702.02560

Total Betti numbers of modules of finite projective dimension

Mark E. Walker
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Abstract

The Buchsbaum-Eisenbud-Horrocks Conjecture predicts that if M is a non-zero module of finite length and finite projective dimension over a local ring R of dimension d, then the i-th Betti number of M is at least d choose i. This conjecture implies that the sum of all the Betti numbers of such a module must be at least 2^d. We prove the latter holds in a large number of cases.

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Mark E. Walker. 2017-02-08. Total Betti numbers of modules of finite projective dimension. https://arxiv.org/abs/1702.02560

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