An example of an infinite set of associated primes of a local cohomology module

Details An example of an infinite set of associated primes of a local cohomology module An example of an infinite set of associated primes of a local cohomology module

2002-09-25

arxiv.org/abs/math/0209353v1

Journal of Algebra, 252 (2002) pp. 161-166

Mathematics

Commutative Algebra

Scientific paper

Let $(R,m)$ be a local Noetherian ring, let $I\subset R$ be any ideal and let $M$ be a finitely generated $R$-module. In 1990 Craig Huneke conjectured that the local cohomology modules $H^i_I(M)$ have finitely many associated primes for all $i$. In this paper I settle this conjecture by constructing a local cohomology module of a local $k$-algebra with an infinite set of associated primes, and I do this for any field $k$.

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