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

Authors:
M. Brodmann, S. Fumasoli and R. Tajarod

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

Published electronically:
April 21, 2003

MathSciNet review:
1993202

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a homogeneous Noetherian ring with local base ring and let be a finitely generated graded -module. Let be the -th local cohomology module of with respect to . If , the -modules , and are Artinian for all . As a consequence, much can be said on the asymptotic behaviour of the -modules for .

**[B-He]**BRODMANN, M., HELLUS, M., Cohomological patterns of coherent sheaves over projective schemes, Journal of Pure and Applied Algebra 172 (2002), 165-182.**[B-K-S]**BRODMANN, M., KATZMAN, M., SHARP, R.Y., Associated primes of graded components of local cohomology modules, Transactions of the AMS 354 (2002), 4261-4283.**[B-M-M]**BRODMANN, M., MATTEOTTI, C., MINH, N.D., Bounds for cohomological deficiency functions of projective schemes over artinian rings, to appear in Vietnam Journal of Mathematics.**[B-S]**BRODMANN, M., SHARP, R.Y., Local cohomology: an algebraic introduction with geometric applications, Cambridge studies in advanced mathematics 60, Cambridge University Press (1998). MR**99h:13020****[B-H]**BRUNS, W., HERZOG, J., Cohen Macaulay rings, Cambridge studies in advanced mathematics 39, Cambridge University Press (1993). MR**95h:13020****[K]**KATZMAN, M., An example of an infinite set of associated primes of a local cohomology module, Journal of Algebra 252 (2002), 161-166.**[Ki]**KIRBY, D., Artinian modules and Hilbert polynomials, Quart. J. Math. Oxford Ser. (2) 24 (1973) 47-57. MR**47:4993****[S]**SINGH, A.K., -torsion elements in local cohomology modules, Math. Res. Lett. 7 (2000) 165-176. MR**2001g:13039**

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Additional Information

**M. Brodmann**

Affiliation:
Institute of Mathematics, University of Zurich, Winterthurerstrasse 190, CH – 8057 Zürich, Switzerland

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

Email:
roshan@iranpasargad.net

DOI:
https://doi.org/10.1090/S0002-9939-03-07009-6

Keywords:
Local cohomology modules,
Artinian modules,
graded components

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

Article copyright:
© Copyright 2003
American Mathematical Society