Generators of D-modules in positive characteristic

Josep Alvarez-Montaner, Manuel Blickle, Gennady Lyubeznik

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

Let R = k[x1,..., xd] or R = k[[x1,..., xd]] 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 R|k be the ring of k-linear differential operators of R. In this paper we prove that if f is a non-zero element of R then Rf, obtained from R by inverting f, is generated as a DR|k-module by 1/f. This is an amazing fact considering that the corresponding characteristic zero statement is very false. In fact we prove an analog of this result for a considerably wider class of rings R and a considerably wider class of D R|k-modules.

Original languageEnglish (US)
Pages (from-to)459-473
Number of pages15
JournalMathematical Research Letters
Volume12
Issue number4
DOIs
StatePublished - Jul 2005

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