Bivariate Hilbert Functions for the Torsion Functor

2004/10/13 by Emanoil Theodorescu
Mathematics · #math.AC #msc:13D40

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published as Journal of Algebra (265), 2003

arxiv created 2004/10/13 · arxiv updated 2009/12/01

Abstract

Let (R,P) be a commutative, local Noetherian ring, I, J ideals, M and N finitely generated R-modules. Suppose J + ann_R M + ann_R N is P-primary. The main result of this paper is Theorem 6, which gives necessary and sufficient conditions for the length of \t_i(M/IⁿM,N/J^mN), to agree with a polynomial, for m, n ≫ 0. As a corollary, it is shown that the length of \t_i(M/IⁿM,N/IⁿN)) always agrees with a polynomial in n, for n ≫ 0, provided I + ann_R M + ann_R N is P-primary.

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