Decent intersection and Tor-rigidity for modules over local hypersurfaces
Hailong Dao
Abstract
We study two properties of modules over a local hypersurface R: decency and rigidity. We show that the vanishing of Hochster's function θR(M,N), known to imply decent intersection, also implies rigidity. We investigate the vanishing of θR(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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