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Free resolutions of parameter ideals for some rings with finite local cohomology


Author: Hamidreza Rahmati
Journal: Proc. Amer. Math. Soc. 136 (2008), 467-474
MSC (2000): Primary 13D02, 13D40; Secondary 13H10
DOI: https://doi.org/10.1090/S0002-9939-07-09127-7
Published electronically: November 3, 2007
MathSciNet review: 2358485
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Abstract: Let $ R$ be a $ d$-dimensional local ring, with maximal ideal $ \mathfrak{m}$, containing a field and let $ x_1, \dots , x_d$ be a system of parameters for $ R$. If $ \operatorname{depth}\,R \geq d - 1$ and the local cohomology module $ \operatorname{H}_{\mathit{m}}^{d-1}(R)$ is finitely generated, then there exists an integer $ n$ such that the modules $ R/(x_1^i,\dots,x_d^i)$ have the same Betti numbers, for all $ i\geq n$.


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Additional Information

Hamidreza Rahmati
Affiliation: Department of Mathematics, University of Nebraska, Lincoln, Nebraska 68588
Email: hrahmati@math.unl.edu

DOI: https://doi.org/10.1090/S0002-9939-07-09127-7
Received by editor(s): April 12, 2006
Received by editor(s) in revised form: January 12, 2007
Published electronically: November 3, 2007
Additional Notes: This research was partly supported by NSF grant DMS-0201904
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2007 American Mathematical Society

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