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
SN - 1073-2780
VL - 12
SP - 459
EP - 473
JO - Mathematical Research Letters
JF - Mathematical Research Letters
IS - 4
ER -