Decent intersection and Tor-rigidity for modules over local hypersurfaces

2006/11/19 by Hailong Dao, Dao, Hailong
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #math.AC #msc:13D07 #msc:13D22 #msc:14C17

paper · pdf · doi:10.48550/arxiv.math/0611568

Many minor changes including title

arxiv created 2011/02/24 · arxiv updated 2011/02/25

Abstract

We study two properties of modules over a local hypersurface R: decency and rigidity. We show that the vanishing of Hochster's function θ^R(M,N), known to imply decent intersection, also implies rigidity. We investigate the vanishing of θ^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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