Geodesic
Total Betti numbers of modules of finite projective dimension
Mark E. Walker1
1 University of Nebraska, Lincoln, NE
Annals of mathematics, Tome 186 (2017) no. 2, pp. 641-646.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.
DOI : 10.4007/annals.2017.186.2.6

Mark E. Walker 1

1 University of Nebraska, Lincoln, NE 
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Mark E. Walker. Total Betti numbers of modules of finite projective dimension. Annals of mathematics, Tome 186 (2017) no. 2, pp. 641-646. doi : 10.4007/annals.2017.186.2.6. http://geodesic.mathdoc.fr/articles/10.4007/annals.2017.186.2.6/

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