A survey on the Arveson-Douglas conjecture (Q2220159)

The Arveson-Douglas conjecture refers to a set of conjectures involving essential normality of submodules and quotient modules of analytic function spaces. In this survey, the authors describe several proven results over the past 50 years related to this conjecture. These results are complemented with questions related to the discussed topics. These topics include geometric invariants for row contractions, index theorems, holomorphic extension theorems, principal submodules, decomposition modules, the geometric Arveson-Douglas conjecture, decomposition of submodules and quotient modules, and quotient modules over the polydisc, among others. For the entire collection see [Zbl 1455.47001].