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, Volume 156, Issue 1–2, pp 81–115 | Cite as

Unipotent monodromy and arithmetic \({\mathcal {D}}\)-modules

  • Daniel CaroEmail author


In the framework of Berthelot’s theory of arithmetic \({\mathcal {D}}\)-modules, we introduce the notion of arithmetic \({\mathcal {D}}\)-modules having potentially unipotent monodromy. For example, from Kedlaya’s semistable reduction theorem, the overconvergent isocrystals with Frobenius structure have potentially unipotent monodromy. We construct some coefficients stable under Grothendieck’s six operations, containing overconvergent isocrystals with Frobenius structure and whose objects have potentially unipotent monodromy. On the other hand, we introduce the notion of arithmetic \({\mathcal {D}}\)-modules having quasi-unipotent monodromy. These objects are overholonomic, contain the isocrystals having potentially unipotent monodromy and are stable under Grothendieck’s six operations and under base change.

Mathematics Subject Classification

14F10 14F30 


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Universite de Caen NormandieCaenFrance

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