Extending meromorphic connections to coadmissible D-cap-modules

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.

arXiv comment21 pages. To appear in Crelle's Journal

References in corpus (1)

• D-modules on rigid analytic spaces III: Weak holonomicity and operations