Holonomicity versus weak holonomicity

Determine whether holonomicity implies weak holonomicity for coadmissible modules over Ardakov–Wadsley’s sheaf of infinite-order differential operators in the rigid analytic setting.

Background

The paper distinguishes two finiteness notions for coadmissible modules over Ardakov–Wadsley’s sheaf of differential operators: weak holonomicity, defined through the vanishing of Ext-groups outside the middle degree, and holonomicity, defined functorially and designed to be stable under operations in the rigid analytic module formalism. The relationship between these notions is not established.

Resolving this question would clarify whether the stronger functorial notion of holonomicity automatically yields the homological finiteness property needed for weak holonomicity.