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

Abstract

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 $k$.