Decent intersection and Tor-rigidity for modules over local hypersurfaces

Dao, Hailong

doi:10.1090/S0002-9947-2012-05574-7

Decent intersection and Tor-rigidity for modules over local hypersurfaces
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Abstract:

We study two properties for a pair of finitely generated modules over a local hypersurface $R$: decency, which is close to proper intersection of the supports, and $\operatorname {Tor}$-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. Many applications are given.

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