Homology, Homotopy and Applications

Volume 4 (2002)

Number 2

The Roos Festschrift volume

An analogue of holonomic D-modules on smooth varieties in positive characteristics

Pages: 83 – 116

DOI: https://dx.doi.org/10.4310/HHA.2002.v4.n2.a5


Rikard Bögvad (Department of Mathematics, University of Stockholm, Sweden)


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.


ring of differential operators, positive characteristics, holonomic, F-finite module

2010 Mathematics Subject Classification

14F10, 16S32, 32C38

Published 1 January 2002