Lyubeznik's finite-associated-primes conjecture

Let $R$ be a regular ring, let $\mathfrak{a}$ be an ideal of $R$, and let $H^i_\mathfrak{a}(R)$ denote its $i$th local cohomology module. Lyubeznik's conjecture. The module $H^i_\mathfrak{a}(R)$ has finitely many associated prime ideals.

This conjecture has been settled for unramified regular local rings by results of Huneke–Sharp and Lyubeznik, but remains open for polynomial rings over the integers.