Hostname: page-component-8448b6f56d-sxzjt Total loading time: 0 Render date: 2024-04-24T07:18:29.454Z Has data issue: false hasContentIssue false
  • English
  • Français

Derived functors and Hilbert polynomials

Published online by Cambridge University Press:  31 January 2002

EMANOIL THEODORESCU
EMANOIL THEODORESCU
Affiliation:
Department of Mathematics, University of Kansas, Lawrence, KS 66045, USA. e-mail: theodore@math.ukans.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Let R be a commutative Noetherian ring, I an ideal, M and N finitely generated R-modules. Assume V(I) [xcap ] Supp (M) [xcap ] Supp (N) consists of finitely many maximal ideals and let λ(Exti(N/InN, M)) denote the length of Exti(N/InN, M). It is shown that λ(Exti(N/InN, M)) agrees with a polynomial in n for n [Gt ] 0, and an upper bound for its degree is given. On the other hand, a simple example shows that some special assumption such as the support condition above is necessary in order to conclude that polynomial growth holds.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 132 , Issue 1 , January 2002 , pp. 75 - 88
Copyright
2002 Cambridge Philosophical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)