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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Decent intersection and Tor-rigidity for modules over local hypersurfaces


Author: Hailong Dao
Journal: Trans. Amer. Math. Soc. 365 (2013), 2803-2821
MSC (2010): Primary 13D07, 13D22, 14C17
Published electronically: November 1, 2012
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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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Additional Information

Hailong Dao
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045-7523
Email: hdao@math.ku.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05574-7
PII: S 0002-9947(2012)05574-7
Keywords: Local rings, hypersurfaces, Tor-rigidity, intersection multiplicity, decent intersection
Received by editor(s): April 3, 2010
Received by editor(s) in revised form: August 19, 2010, and February 21, 2011
Published electronically: November 1, 2012
Additional Notes: The author was partially supported by NSF grant 0834050
Article copyright: © Copyright 2012 American Mathematical Society