Proceedings of the American Mathematical Society

Author(s): M. P. Brodmann; A. Lashgari Faghani
Journal: Proc. Amer. Math. Soc. 128 (2000), 2851-2853.
MSC (2000): Primary 13D45; Secondary 13E99
Posted: April 28, 2000
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We show that the first non-finitely generated local cohomology module $H^i_\mathfrak{a} (M)$ of a finitely generated module

over a noetherian ring

with respect to an ideal $\mathfrak{a}\subseteq R$ has only finitely many associated primes.

[B-R-Sh]: Brodmann, M., Rotthaus, Ch., Sharp, R., On annihilators and associated primes of local cohomology modules, to appear in Journal of Pure and Applied Algebra
[B-Sh]: Brodmann, M, Sharp, R., Local cohomology - an algebraic introduction with geometric applications, Cambridge studies in advanced mathematics No. 60, Cambridge University Press, 1998 CMP 98:10
[F]: Faltings, G., Der Endlichkeitssatz in der lokalen Kohomologie, Mathematische Annalen 255 (1981), 45-56 MR 82f:13003
[K]: Katzman, M., Finiteness of $\cup_e {\mathrm Ass} F^e (M)$ and its connections to tight closure; Illinois Journal of Mathematics 40 (1996), 330-337 MR 97i:13003
[M-S]: Melkersson, L., Schenzel, P., Asymptotic prime ideals related to derived functors; Proc. AMS 117, No 4 (1993), 935- 938 MR 93e:13027
[R]: Raghavan, K.N., Local-global principle for annihilation of local cohomology; Contemporary Math. 159 (1994), 329-331 MR 95c:13018

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 13D45, 13E99

M. P. Brodmann
Affiliation: Mathematical Institute, University of Zurich, Zurich, Switzerland
Email: brodmann@math.unizh.ch

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