Geodesic
An analogue of holonomic D-modules on smooth varieties in positive characteristics
Homology, homotopy, and applications, Tome 4 (2002) no. 2, pp. 83-116.

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In this paper a definition of a category of modules over the ring of differential operators on a smooth variety of finite type in positive characteristics is given. It has some of the good properties of holonomic D-modules in zero characteristic. We prove that it is a Serre category and that it is closed under the usual D-module functors, as defined by Haastert. The relation to the similar concept of F-finite modules, introduced by Lyubeznik, is elucidated, and several examples, such as étale algebras, are given.
DOI : 10.4310/HHA.2002.v4.n2.a5
Classification : 14F10, 16S32, 32C38
Keywords: ring of differential operators, positive characteristics, holonomic, F-finite module 
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     title = {An analogue of holonomic {D-modules} on smooth varieties in positive characteristics},
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     pages = {83--116},
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Rikard Bögvad. An analogue of holonomic D-modules on smooth varieties in positive characteristics. Homology, homotopy, and applications, Tome 4 (2002) no. 2, pp. 83-116. doi : 10.4310/HHA.2002.v4.n2.a5. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2002.v4.n2.a5/

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