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arXiv · 1812.05000

Extending meromorphic connections to coadmissible D-cap-modules

Thomas Bitoun·Andreas Bode
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Abstract

We investigate when a meromorphic connection on a smooth rigid analytic variety $X$ gives rise to a coadmissible $\mathcal{D}_X$-cap-module, and show that this is always the case when the roots of the corresponding $b$-functions are all of positive type. On the other hand, we also give an example of an integrable connection on the punctured unit disk whose pushforward is not a coadmissible module.

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Thomas Bitoun, Andreas Bode. 2018-12-12. Extending meromorphic connections to coadmissible D-cap-modules. https://arxiv.org/abs/1812.05000

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