Hilbert-Samuel polynomials for the contravariant extension functor

Andrew Crabbe; Daniel Katz; Janet Striuli; Emanoil Theodorescu

doi:10.1215/00277630-2009-005

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Home > Journals > Nagoya Math. J. > Volume 198 > Article

June 2010 Hilbert-Samuel polynomials for the contravariant extension functor

Andrew Crabbe, Daniel Katz, Janet Striuli, Emanoil Theodorescu

Nagoya Math. J. 198: 1-22 (June 2010). DOI: 10.1215/00277630-2009-005

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Abstract

Let $(R,\mathfrak {m})$ 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 $\operatorname{Ext}^{i}_{R}(M,N/\mathfrak{m}^{n}N)$ . A number of corollaries are given, and more general filtrations are also considered.

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Andrew Crabbe. Daniel Katz. Janet Striuli. Emanoil Theodorescu. "Hilbert-Samuel polynomials for the contravariant extension functor." Nagoya Math. J. 198 1 - 22, June 2010. https://doi.org/10.1215/00277630-2009-005

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Published: June 2010

First available in Project Euclid: 10 May 2010

zbMATH: 1231.13011

MathSciNet: MR2666575

Digital Object Identifier: 10.1215/00277630-2009-005

Subjects:

Primary: 13C11 , 13D07 , 13D40 , 13H15

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Vol.198 • June 2010

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Andrew Crabbe, Daniel Katz, Janet Striuli, Emanoil Theodorescu "Hilbert-Samuel polynomials for the contravariant extension functor," Nagoya Mathematical Journal, Nagoya Math. J. 198(none), 1-22, (June 2010)

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