Generators of D-modules in positive characteristic

Details Generators of D-modules in positive characteristic Generators of D-modules in positive characteristic

2005-02-18

arxiv.org/abs/math/0502405v1

Math. Res. Lett. 12 (2005), no. 4, 459--473

Mathematics

Commutative Algebra

15 pages. combines and extends the results of math.AC/0407464 and math.AC/0408124. to appear in Mathematical Research Letters

Scientific paper

Let R be either a polynomial or a formal power series ring in a finite number of variables over a field k of characteristic p > 0 and let D be the ring of klinear differential operators of R. In this paper we prove that if f is a non-zero element of R then R[1/f], obtained from R by inverting f, is generated as a D-module by 1/f . This is very much in contrast to the characteristic zero situation where the corresponding statement is false (there the generation is governed by the roots of the Bernstein polynomial of f). In fact we prove analogs of the above result for a considerably wider class of rings R and a considerably wider class of D-modules.

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