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Derived functors and Hilbert polynomials
Published online by Cambridge University Press: 31 January 2002
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
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