Decent intersection and Tor-rigidity for modules over local hypersurfaces

Details Decent intersection and Tor-rigidity for modules over local hypersurfaces Decent intersection and Tor-rigidity for modules over local hypersurfaces

2006-11-19

arxiv.org/abs/math/0611568v4

Mathematics

Commutative Algebra

Many minor changes including title

Scientific paper

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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