preprint Takuma Hayashi author Fabian Januszewski author 81636 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. 2023 eng 1808.10709 170 Hayashi, Takuma, and Fabian Januszewski. “Families of Twisted D-Modules and Arithmetic Models of  Harish-Chandra Modules.” <i>ArXiv:1808.10709</i>, 2023. T. Hayashi, F. Januszewski, ArXiv:1808.10709 (2023). Hayashi, T., &#38; Januszewski, F. (2023). Families of twisted D-modules and arithmetic models of  Harish-Chandra modules. In <i>arXiv:1808.10709</i>. T. Hayashi and F. Januszewski, “Families of twisted D-modules and arithmetic models of  Harish-Chandra modules,” <i>arXiv:1808.10709</i>. 2023. Hayashi T, Januszewski F. Families of twisted D-modules and arithmetic models of  Harish-Chandra modules. <i>arXiv:180810709</i>. Published online 2023. @article{Hayashi_Januszewski_2023, title={Families of twisted D-modules and arithmetic models of  Harish-Chandra modules}, journal={arXiv:1808.10709}, author={Hayashi, Takuma and Januszewski, Fabian}, year={2023} } Hayashi, Takuma, and Fabian Januszewski. “Families of Twisted D-Modules and Arithmetic Models of  Harish-Chandra Modules.” <i>ArXiv:1808.10709</i>, 2023. 531952024-04-03T17:10:19Z2024-04-03T17:11:07Z