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Hilbert-Samuel polynomials for the contravariant extension functor

Published online by Cambridge University Press:  11 January 2016

Andrew Crabbe ,
Daniel Katz ,
Janet Striuli  and
Emanoil Theodorescu
Andrew Crabbe
Affiliation:
Department of Mathematics, Syracuse University, Syracuse, New York 13244-1150, [email protected]
Daniel Katz
Affiliation:
Department of Mathematics, University of Kansas, Lawrence, Kansas 66045, [email protected]
Janet Striuli
Affiliation:
Department of Mathematics and Computer Science, Fairfield University, Fairfield, Connecticut 06824, [email protected]
Emanoil Theodorescu
Affiliation:
Division of Statistics, Northern Illinois University, De Kalb, Illinois 60115, [email protected]
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Abstract

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Let (R,m) be a local ring, and let M and N be finite R-modules. In this paper we give a formula for the degree of the polynomial giving the lengths of the modules ExtiR(M,N/mnN). A number of corollaries are given, and more general filtrations are also considered.

Keywords

13D0713D4013H1513C11
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 198 , June 2010 , pp. 1 - 22
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2010

References

[1] Corso, A., Huneke, C., Katz, D., and Vasconcelos, W., Integral closure of ideals and annihilators of homology, Lect. Notes Pure Appl. Math. 227 (2005), 33–48.Google Scholar
[2] Crabbe, A. and Striuli, J., Constructing big indecomposable modules, Proc. Amer. Math. Soc. 137 (2009), 2181–2189.Google Scholar
[3] Iyengar, S. and Puthenpurakal, T., Hilbert-Samuel functions of modules over Cohen-Macaulay local rings, Proc. Amer. Math. Soc. 135 (2007), 637–648.Google Scholar
[4] Goto, S., Hayasaka, F., and Takahashi, R., On vanishing of certain Ext modules, J. Math. Soc. Japan 60 (2008), 1045–1064.Google Scholar
[5] Katz, D. and Theodorescu, E., On the degree of Hilbert polynomials associated to the torsion functor, Proc. Amer. Math. Soc. 135 (2007), 3073–3082.Google Scholar
[6] Kodiyalam, V., Homological invariants of powers of an ideal, Proc. Amer. Math. Soc. 118 (1993), 757–764.Google Scholar
[7] Theodorescu, E., Derived functors and Hilbert polynomials, Math. Proc. Cambridge Philos. Soc. 132 (2002), 75–88.Google Scholar