Homology, Homotopy and Applications

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

Rikard Bögvad

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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 etale algebras, are given.

Article information

Homology Homotopy Appl., Volume 4, Number 2 (2002), 83-116.

First available in Project Euclid: 13 February 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14F10: Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials [See also 13Nxx, 32C38]
Secondary: 16S32: Rings of differential operators [See also 13N10, 32C38] 32C38: Sheaves of differential operators and their modules, D-modules [See also 14F10, 16S32, 35A27, 58J15]


Bögvad, Rikard. An analogue of holonomic D-modules on smooth varieties in positive characteristics. Homology Homotopy Appl. 4 (2002), no. 2, 83--116. https://projecteuclid.org/euclid.hha/1139852458

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