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arXiv · 1807.01086

A Proper Mapping Theorem for coadmissible D-cap-modules

Andreas Bode
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Abstract

We study the behaviour of D-cap-modules on rigid analytic varieties under pushforward along a proper morphism. We prove a D-cap-module analogue of Kiehl's Proper Mapping Theorem, considering the derived sheaf-theoretic pushforward from $\mathcal{D}_X$-cap-modules to $f_*\mathcal{D}_X$-cap-modules for proper morphisms $f: X\to Y$. Under assumptions which can be naturally interpreted as a certain properness condition on the cotangent bundle, we show that any coadmissible $\mathcal{D}_X$-cap-module has coadmissible higher direct images. This implies among other things a purely geometric justification of the fact that the global sections functor in the rigid analytic Beilinson--Bernstein correspondence preserves coadmissibility, and we are able to extend this result to twisted D-cap-modules on analytified partial flag varieties.

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Andreas Bode. 2018-07-03. A Proper Mapping Theorem for coadmissible D-cap-modules. https://arxiv.org/abs/1807.01086

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