Families of twisted $\mathcal D$-modules and arithmetic models of Harish-Chandra modules
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| Format: | Preprint |
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2018
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| _version_ | 1866910506669834240 |
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| author | Hayashi, Takuma Januszewski, Fabian |
| author_facet | Hayashi, Takuma Januszewski, Fabian |
| contents | We develop a theory of tdos and twisted $\mathcal D$-modules over general base schemes with a focus on functorial aspects. In particular, we introduce a flat base change functor and establish its compatibility with globalization and direct image functors. We also study forms of closed $K$-orbits of $θ$-stable parabolic subgroups in the total flag variety. We apply these two developed theories to give a geometric construction of half-integral models of cohomologically induced modules. With a view towards arithmetic applications, we further demonstrate desirable properties of the constructed half-integral models, such as projectivity over the base and torsion-free relative Lie algebra cohomology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1808_10709 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Families of twisted $\mathcal D$-modules and arithmetic models of Harish-Chandra modules Hayashi, Takuma Januszewski, Fabian Representation Theory Algebraic Geometry Primary: 14F10, Secondary: 13N10, 22E47, 32C38 We develop a theory of tdos and twisted $\mathcal D$-modules over general base schemes with a focus on functorial aspects. In particular, we introduce a flat base change functor and establish its compatibility with globalization and direct image functors. We also study forms of closed $K$-orbits of $θ$-stable parabolic subgroups in the total flag variety. We apply these two developed theories to give a geometric construction of half-integral models of cohomologically induced modules. With a view towards arithmetic applications, we further demonstrate desirable properties of the constructed half-integral models, such as projectivity over the base and torsion-free relative Lie algebra cohomology. |
| title | Families of twisted $\mathcal D$-modules and arithmetic models of Harish-Chandra modules |
| topic | Representation Theory Algebraic Geometry Primary: 14F10, Secondary: 13N10, 22E47, 32C38 |
| url | https://arxiv.org/abs/1808.10709 |