TY - JOUR

T1 - Generators of D-modules in positive characteristic

AU - Alvarez-Montaner, Josep

AU - Blickle, Manuel

AU - Lyubeznik, Gennady

PY - 2005/7

Y1 - 2005/7

N2 - 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.

AB - 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.

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U2 - 10.4310/MRL.2005.v12.n4.a2

DO - 10.4310/MRL.2005.v12.n4.a2

M3 - Article

AN - SCOPUS:25144484918

VL - 12

SP - 459

EP - 473

JO - Mathematical Research Letters

JF - Mathematical Research Letters

SN - 1073-2780

IS - 4

ER -