Abstract. We study the existence of nontrivial semidualizing DG modules over tensor products of DG algebras over a field. In particular, this gives a lower bound on the number of semidualizing DG modules over the tensor product.
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.Comment: 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 algebra
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