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

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- by M. Brodmann, S. Fumasoli and R. Tajarod PDF
- Proc. Amer. Math. Soc.
**131**(2003), 2977-2985 Request permission

## Abstract:

Let $R=\bigoplus _{n\geq 0}R_n$ be a homogeneous Noetherian ring with local base ring $(R_0,\mathfrak {m}_0)$ and let $M$ be a finitely generated graded $R$-module. Let $H^i_{R_+}(M)$ be the $i$-th local cohomology module of $M$ with respect to $R_+:=\bigoplus _{n>0}R_n$. If $\dim R_0\leq 1$, the $R$-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 $R_0$-modules $H^i_{R_+}(M)_n$ for $n\rightarrow -\infty$.## References

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## Additional Information

**M. Brodmann**- Affiliation: Institute of Mathematics, University of Zurich, Winterthurerstrasse 190, CH – 8057 Zürich, Switzerland
- MR Author ID: 41830
- Email: brodmann@math.unizh.ch
**S. Fumasoli**- Affiliation: Institute of Mathematics, University of Zurich, Winterthurerstrasse 190, CH – 8057 Zürich, Switzerland
- Email: fumasoli@math.unizh.ch
**R. Tajarod**- Affiliation: Institute of Mathematics, University for Teacher Education, 599 Taleghani Avenue, Tehran 15614, Iran
- MR Author ID: 673912
- Email: roshan@iranpasargad.net
- Received by editor(s): April 16, 2002
- Published electronically: April 21, 2003
- Additional Notes: The third author thanks the University of Zürich for the hospitality offered during the preparation of this paper.
- Communicated by: Bernd Ulrich
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**131**(2003), 2977-2985 - MSC (2000): Primary 13D45, 13E10
- DOI: https://doi.org/10.1090/S0002-9939-03-07009-6
- MathSciNet review: 1993202