The D–module Structure of R[f ]–modules
نویسنده
چکیده
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 SpecR, and F e∗ is the associated pullback functor. It is well known that M then carries a natural DR–module structure. In this paper we investigate the relation between the unit R[F ]–structure and the induced DR–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 DR–module. An example showing the necessity of k being algebraically closed is also given.
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