F. Kasch Modules and rings (translated by D. A. R. Wallace) (Academic Press, London1982), xiii + 372 pp. £33.80.

D-modules over Rings with Finite F-representation Type

Smith and Van den Bergh [29] introduced the notion of finite F-representation type as a characteristic p analogue of the notion of finite representation type. In this paper, we prove two finiteness properties of rings with finite F-representation type. The first property states that if R = L n≥0 Rn is a Noetherian graded ring with finite (graded) F-representation type, then for every non-zerodi...

The D–module Structure of R[f ]–modules

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 ]–stru...

Noncommutative Resolution, F-blowups and D-modules

We explain the isomorphism between the G-Hilbert scheme and the F-blowup from the noncommutative viewpoint after Van den Bergh. In doing this, we immediately and naturally arrive at the notion of D-modules. We also find, as a byproduct, a canonical way to construct a noncommutative resolution at least for a few classes of singularities in positive characteristic.

A 35 , 16 S 99 , 16 S 32 the D – Module Structure of R [ F ] – Modules

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 ]–struct...

Paratactic Semantics (d R a F T !)