Abstract
The Buchsbaum-Eisenbud-Horrocks Conjecture predicts that the $i^{\rm th}$ 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 ${d \choose i}$. It would follow from the validity of this conjecture that $\sum_i \beta_i(M) \geq 2^{d}$. 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.
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author = {Brown, Michael K. and Miller, Claudia and Thompson, Peder and Walker, Mark E.},
title = {Cyclic {A}dams operations},
journal = {J. Pure Appl. Algebra},
fjournal = {Journal of Pure and Applied Algebra},
volume = {221},
number = {7},
year = {2017},
pages = {1589--1613},
zblnumber = {1360.19006},
mrnumber = {3614968},
doi = {10.1016/j.jpaa.2016.12.018},
} -
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