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Nagoya Mathematical Journal

Hilbert-Samuel polynomials for the contravariant extension functor

Andrew Crabbe, Daniel Katz, Janet Striuli, and Emanoil Theodorescu
Source: Nagoya Math. J. Volume 198 (2010), 1-22.

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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Primary Subjects: 13D07, 13D40, 13H15, 13C11
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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.nmj/1273496983
Digital Object Identifier: doi:10.1215/00277630-2009-005
Zentralblatt MATH identifier: 05735942
Mathematical Reviews number (MathSciNet): MR2666575

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Project Euclid: euclid.jmsj/1225894032
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