Families of twisted $\mathcal D$-modules and arithmetic models of Harish-Chandra modules

Fuente: arXiv
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Main Authors: Hayashi, Takuma, Januszewski, Fabian
Format: Preprint
Published: 2018
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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