Quantization of spectral curves and DQ-modules

Given an holomorphic Higgs bundle on a compact Riemann surface of
genus greater than one, we prove the existence of an holonomic DQ-module
supported by the spectral curve associated to this bundle. Then, we relate
quantum curves arising in various situations (quantization of spectral curves
of Higgs Bundles, quantization of the A-polynomial...) to DQ-modules and
show that a quantum curve and the DQ-module canonically associated to it
have isomorphic sheaves of solutions.