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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
DOI: https://doi.org/10.1090/S0002-9939-2010-10530-0
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.


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Additional Information

Yi Zhang
Affiliation: Department of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Email: zhang397@umn.edu

DOI: https://doi.org/10.1090/S0002-9939-2010-10530-0
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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