Lower bounds on projective levels of complexes

Abstract

For an associative ring $R$, the projective level of a complex $F$ is the smallest number of mapping cones needed to build $F$ from projective $R$-modules. We establish lower bounds for the projective level of $F$ in terms of the vanishing of homology of $F$. We then use these bounds to derive a new version of The New Intersection Theorem for level when $R$ is a commutative Noetherian local ring.

To appear in the Journal of Algebra. In this new version, the paper has been rewritten to study projective levels, and to account for the existence of balanced big Cohen-Macaulay algebras