Arveson's essential normality conjecture for quotient Bergman modules

Let $\Omega\subseteq\mathbb{C}^m$ be a bounded strongly pseudoconvex domain with smooth boundary, let $A$ be the algebra of analytic functions under consideration, and let $I$ be an ideal in $A$. Write $I^{\perp}=L^2_a(\Omega)\ominus\overline{I}$, and let

$$T_p=P_{I^{\perp}}M_p|_{I^{\perp}},\qquad p\in A,$$

be the compressed multiplication operators. The module $I^{\perp}$ is essentially normal when all commutators of its fundamental tuple are compact. Arveson's conjecture. $I^{\perp}$ is essentially normal. In other words, all commutators

$$[T_{z_j},T_{z_k}^{*}],\qquad j,k=1,\ldots,m,$$

are compact. This conjecture asks for essential normality of quotient modules arising from ideals in Bergman spaces and is part of the operator-theoretic study of algebraic varieties and their boundary geometry. The supplied text does not state whether it has been resolved.