Holonomicity of cohomology groups of holonomic complexes

Prove that each cohomology group of a holonomic complex of coadmissible modules over Ardakov–Wadsley’s sheaf is holonomic.

Background

The main holonomicity theorem is formulated for complexes, whereas the desired stronger conclusion concerns the individual higher direct-image modules $R^i j_*\mathcal E^q$. The paper explains that passing from a holonomic complex to its cohomology groups requires an additional unresolved property.

A positive answer, together with stability of weak holonomicity under projective direct images, would establish holonomicity for the individual Gauss–Manin higher pushforwards beyond the strict normal-crossing setting.