Extending compatibility beyond Z/pα and removing p-torsion freeness

Extend the compatibility construction of the q-Hodge filtration to rings beyond Z/p^α, ideally removing the p-torsion freeness requirement in Theorem 2.8(1), by developing methods that do not rely on strict control of nilpotent elements specific to Z/p^α.

Background

The authors’ explicit compatibility argument crucially uses special features of Z/p^α, notably control over nilpotent elements. They point out that generalizing this argument to broader classes of rings—especially when p-torsion freeness fails—remains out of reach with current techniques.

A general extension would strengthen the functorial and structural framework for q-Hodge filtrations developed in the paper.