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A property of local cohomology modules of polynomial rings

Author: Yi Zhang
Journal: Proc. Amer. Math. Soc. 139 (2011), 125-128
MSC (2010): Primary 13D45
Published electronically: August 3, 2010
MathSciNet review: 2729076
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Abstract: Let $ R=k[x_1,\cdots, x_n]$ be a polynomial ring over a field $ k$ of characteristic $ p>0,$ and let $ I=(f_1,\cdots,f_s)$ be an ideal of $ R.$ We prove that every associated prime $ P$ of $ H^i_I(R)$ satisfies dim$ R/P\geqslant n-\sum$deg$ f_i.$ In characteristic 0 the question is open.

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

  • 1. M. F. Atiyah, I. G. Macdonald, Introduction to commutative algebra. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969. MR 0242802 (39:4129)
  • 2. G. Lyubeznik, $ F$-modules: Applications to local cohomology and $ D$-modules in characteristic $ p>0$. J. Reine Angew. Math. 491 (1997), 65-130. MR 1476089 (99c:13005)
  • 3. G. Lyubeznik, W. Zhang, Y. Zhang, A property of the Frobenius map of a polynomial ring. Preprint, arXiv: 1001.2949.
  • 4. I. Peeva, M. Stillman, Open problems on syzygies and Hilbert functions. J. Commut. Algebra 1 (2009), no. 1, 159-195. MR 2462384 (2009i:13024)

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Additional Information

Yi Zhang
Affiliation: Department of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455

Received by editor(s): March 29, 2010
Published electronically: August 3, 2010
Additional Notes: NSF support through grant DMS-0701127 is gratefully acknowledged.
Communicated by: Irena Peeva
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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