The D-Module structure of R[F]-modules

Details The D-Module structure of R[F]-modules The D-Module structure of R[F]-modules

2002-01-19

arxiv.org/abs/math/0201180v2

Trans. Am. Math. Soc 355 (2003), 4, 1647-1668

Mathematics

Algebraic Geometry

25 pages. Some minor changes following referee's suggestion. To appear in Trans. AMS

Scientific paper

Let R be a regular ring essentially of finite type over a perfect field k. An R-module M is called a unit R[F]-module if it comes equipped with an isomorphism F*M-->M where F denotes the Frobenius map on Spec R, and F* is the associated pullback functor. It is well known that M then carries a natural D-module structure. In this paper we investigate the relation between the unit R[F]-structure and the induced D-structure on M. In particular, it is shown that, if k is algebraically closed and M is a simple finitely generated unit R[F]-module, then it is also simple as a D-module. An example showing the necessity of k being algebraically closed is also given.

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