  This paper continues our study of the sheaf associated to K\"ahler
differentials in the cdh-topology and its cousins, in positive characteristic,
without assuming resolution of singularities. The picture for the sheaves
themselves is now fairly complete. We give a calculation $\mathcal{O}_{cdh}(X)
\cong \mathcal{O}(X^{sn})$ in terms of the seminormalisation. We observe that
the category of representable cdh-sheaves is equivalent to the category of
seminormal varieties. We conclude by proposing some possible connections to
Berkovich spaces, and $F$-singularities in the last section. The tools
developed for the case of differential forms also apply in other contexts and
should be of independent interest.
