Huneke's conjecture on associated primes of local cohomology modules

Let $R$ be a Noetherian local ring, let $M$ be a finitely generated $R$-module, let $I$ be an ideal of $R$, and write ${\rm H}^i_I(M)$ for the $i$-th local cohomology module of $M$ with support in $I$. Huneke's conjecture. For each $i\geq 0$, the $R$-module ${\rm H}^i_I(M)$ has finitely many associated primes.

Huneke proposed this conjecture in 1990. It is refuted in general by known counterexamples, although it has been confirmed in several cases, including when the dimension is at most three; the paper studies further cases for factorial domains.