  In this paper, we apply Clausen-Scholze's theory of solid modules to the
existence of adelic decompositions for schemes of finite type over
$\mathbb{Z}$. Specifically, we use the six-functor formalism for solid modules
to define the skeletal filtration of a scheme, and then we show that
decomposing a quasi-coherent sheaf with respect to this filtration gives rise
to a new construction of the Beilinson-Parshin adelic resolution.
