Families of twisted D-modules and arithmetic models of Harish-Chandra modules

We develop a theory of tdos and twisted $\mathcal D$-modules over general bases with an emphasis on functorial aspects. In particular, we establish a flat base change theorem as well as faithfully flat descent for twisted $\mathcal D$-modules. We define (derived) inverse and direct images of twisted $\mathcal D$-modules and investigate how these functors behave under base change. We also discuss forms of closed $K$-orbits attached to $\theta$-stable parabolic subgroups. These results imply the existence of models of cohomologically induced modules over general fields of characteristic 0 and even half-integer rings, whose study is motivated by potential applications to number theory in the literature.