We establish a derived functor characterization of the relative Spencer hypercohomology associated with a D -algebra corresponding to a formally integrable system of algebraic differential equations. Roughly speaking, this result can be interpreted as describing the global variation of solutions for the associated family of partial differential equations across fibers. Additionally, we provide an equivalent formulation in terms of a suitable Hochschild hypercohomology of the corresponding cosymbolic comodule.
Kryczka et al. (2025) studied this question.