Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Is there a good notion of holonomic $D$-modules on rigid analytic spaces?

share|improve this question

1 Answer 1

Yes. Although it is only beginning to be developed.

You probably want to start with Berthelot: D-modules arithmétiques I : Opérateurs différentiels de niveau fini and Introduction à la théorie arithmétique des D-modules, and other papers that can be found at http://perso.univ-rennes1.fr/pierre.berthelot/ Section 5 of the second paper I mentioned is perhaps most relevant.

There is also a recent paper of Caro which I cannot find online called 'Holonomie sans structure de Frobenius et criteres d'Holonomie' which removes the necessity of the Frobenius action from Berhelot's work. I suppose he would send you a copy of upon request.

Finally, in a piece of shameless self-advertising, Konstantin Ardakov and I recently put a preprint on the arXiv http://arxiv.org/abs/1102.2606 part of which seeks to find a framework to further develop the theory.

Update: Caro's paper mentioned above now seems to be available here: http://aif.cedram.org/item?id=AIF_2011__61_4_1437_0 although you need a subscription to access it.

share|improve this answer
Incidentally, a more specific question might yield a more specific answer. –  Simon Wadsley Mar 1 '11 at 11:10

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.