Permanent URL to this publication: http://dx.doi.org/10.5167/uzh21680
Brodmann, M; Rohrer, F (2005). HilbertSamuel coefficients and postulation numbers of graded components of certain local cohomology modules. Proceedings of the American Mathematical Society, 133(4):987993 (electronic).

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Abstract
Let $R=\bigoplus_{n\ge 0}R_n$ be a positively graded commutative Noetherian ring with onedimensional local base ring $(R_0,\germ{m}_0)$. Let $\germ{q}_0\subseteq R_0$ be an $\germ{m}_0$primary ideal. Let $M$ be a finitely generated graded $R$module and let $i\in\Bbb N_0$. Let $H^i_{R_+}(M)$ denote the $i$th local cohomology module of $M$ with respect to the irrelevant ideal $R_+=\bigoplus_{n>0}R_n$ of $R$. The main results in this paper are: \roster \item"(a)" Assume that $\dim_{R_0}(H^i_{R_+}(M)_n)=1$ for all $n\ll 0$. Then there is a polynomial $S(x)\in\Bbb Q[x]$ of degree $<i$ such that for all $n\ll 0$, $$e_1(\germ{q}_0,H^i_{R_+}(M)_n)=S(n),$$ where $e_1(\germ{q}_0,H^i_{R_+}(M)_n)$ is the socalled first HilbertSamuel coefficient of $H^i_{R_+}(M)_n$ with respect to $\germ{q}_0$. \item"(b)" There is some $c\in\Bbb N_0$ such that $\mu(\germ{q}_0,H^i_{R_+}(M)_n)\le c$ for all $n\in\Bbb Z$, where $\mu(\germ{q}_0,H^i_{R_+}(M)_n)$ is the postulation number of the $R_0$module $H^i_{R_+}(M)_n$ with respect to $\germ{q}_0$. \endroster
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Additional indexing
Item Type:  Journal Article, refereed, original work 

Communities & Collections:  07 Faculty of Science > Institute of Mathematics 
Dewey Decimal Classification:  510 Mathematics 
Uncontrolled Keywords:  Local cohomology modules, graded components, HilbertSamuel polynomials 
Language:  English 
Date:  2005 
Deposited On:  03 Feb 2010 08:42 
Last Modified:  09 Jan 2014 09:59 
Publisher:  American Mathematical Society 
ISSN:  00029939 
Additional Information:  First published in [Proc. Amer. Math. Soc. 133 (2005), no. 4, 987993 (electronic)], published by the American Mathematical Society 
Publisher DOI:  10.1090/S0002993904077792 
Related URLs:  http://www.ams.org/mathscinetgetitem?mr=2117198 
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