The geometric Arveson–Douglas conjecture for homogeneous varieties

Let $M$ be a homogeneous variety in the unit ball $\mathbb{B}_n$. Define

$$P=\{f\in L_a^{2}(\mathbb{B}_n): f|_M=0\}$$

and let

$$Q=P^{\perp}=\overline{\operatorname{span}}\{K_{\lambda}:\lambda\in M\}.$$

Here $K_{\lambda}$ denotes the reproducing kernel at $\lambda$.

Geometric Arveson–Douglas conjecture. The quotient module $Q$ is $p$-essentially normal for every $p>\dim M$.

This is the geometric version of the Arveson–Douglas conjecture, obtained by considering submodules of functions vanishing on a variety. It is related to the ideal formulation when the ideal is radical and its closure agrees with the vanishing submodule. The supplied text gives no resolution status.