Decent intersection and Tor-rigidity for modules over local hypersurfaces

Abstract

We study two properties of modules over a local hypersurface $R$: decency and rigidity. We show that the vanishing of Hochster's function ${\theta }^R(M,N)$, known to imply decent intersection, also implies rigidity. We investigate the vanishing of ${\theta }^R(M,N)$ to obtain new results about decency and rigidity over hypersurfaces. We employ a mixture of techniques from Commutative Algebra and Intersection Theory of algebraic cycles.

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References in corpus (1)

• Asymptotic behavior of Tor over complete intersections and applications

Cited by in corpus (1)

• The vanishing of a higher codimension analog of Hochster's theta invariant