## Integral $$p$$-adic differential modules.(English)Zbl 1158.13009

Bertrand, Daniel (ed.) et al., Groupes de Galois arithmétique et différentiels. Paris: Société Mathématique de France (ISBN 978-2-85629-222-8/pbk). Séminaires et Congrès 13, 263-292 (2006).
Summary: An integral (or bounded) local D-module is a differential module over a local D-ring $$R$$ having congruence solution bases over $$R$$. In case $$R$$ is equipped with an iterative derivation, such a D-module is an iterative differential module (ID-module) over $$R$$. In this paper we solve the connected inverse Galois problem for integral D-modules over fields of analytic elements $$K\{t\}$$. In case the residue field of $$K$$ is algebraically closed, we are able to additionally solve the non-connected inverse Galois problem. Further, we study the behaviour of ID-modules by reduction of constants.
For the entire collection see [Zbl 1108.12001].

### MSC:

 13N05 Modules of differentials 12H25 $$p$$-adic differential equations