Abstract: We discuss the Arveson-Douglas conjecture for monomial ideals in Bergman spaces, which is a statement about the compactness of commutators for Hilbert module actions. This special (monomial) case of the conjecture was solved by Arveson (for Drury-Arveson spaces), and Douglas (for Bergman spaces). Our method is different from theirs, and is based on the idea of resolving Hilbert modules. This is joint work with Ronald Douglas and Xiang Tang.
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