Lyubeznik's finiteness conjecture for associated primes of Lyubeznik functors

Let $R$ be a regular ring. A Lyubeznik functor on $R$ is a functor built from local cohomology functors with support in locally closed subsets of $\operatorname{Spec}(R)$, as in Lyubeznik's definition.

Lyubeznik's conjecture. For every Lyubeznik functor $T(\,\cdot\,)$ on $R$, the module $T(R)$ has finitely many associated prime ideals.

This is a generalization of the Huneke–Lyubeznik conjecture, since Lyubeznik functors include compositions of local cohomology functors. The paper proves new cases, while the conjecture remains open in general.