Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Published electronically: November 3, 2007
MathSciNet review: 2358485
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 13D02, 13D40, 13H10

Retrieve articles in all journals with MSC (2000): 13D02, 13D40, 13H10


Additional Information

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

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09127-7
PII: S 0002-9939(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