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Local cohomology over homogeneous rings with one-dimensional local base ring

Authors:	M Brodmann S Fumasoli R Tajarod

Institution:	Institute of Mathematics, University of Zurich, Winterthurerstrasse 190, CH -- 8057 Zürich, Switzerland ; Institute of Mathematics, University of Zurich, Winterthurerstrasse 190, CH -- 8057 Zürich, Switzerland ; Institute of Mathematics, University for Teacher Education, 599 Taleghani Avenue, Tehran 15614, Iran

Abstract:	Let $R=\bigoplus_{n\geq0}R_n$ be a homogeneous Noetherian ring with local base ring $(R_0,\mathfrak{m}_0)$ and let be a finitely generated graded -module. Let $H^i_{R_+}(M)$ be the -th local cohomology module of with respect to $R_+:=\bigoplus_{n>0}R_n$ . If $\dim R_0\leq1$ , the -modules $\Gamma_{\mathfrak{m}_0R}(H^i_{R_+}(M))$ , $(0:_{H_{R_+}^i(M)}\mathfrak{m}_0)$ and $H^i_{R_+}(M)/\mathfrak{m}_0H^i_{R_+}(M)$ are Artinian for all $i\in\mathbb{N} _0$ . As a consequence, much can be said on the asymptotic behaviour of the -modules $H^i_{R_+}(M)_n$ for $n\rightarrow -\infty$ .

Keywords:	Local cohomology modules Artinian modules graded components

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