  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 $k$.
