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A surprising fact about D-modules in characteristic p>0

Josep Alvarez Montaner·Gennady Lyubeznik
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Abstract

Let R=k[x_1,...,x_d] be the polynomial ring in d independent variables, where k is a field of characteristic p>0. Let D be the ring of k-linear differential operators of R and let f be a polynomial in R. In this work we prove that the localization R[1/f] obtained from R by inverting f is generated as a D-module by 1/f. This is an amazing fact considering that the corresponding characteristic zero statement is very false.

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Josep Alvarez Montaner, Gennady Lyubeznik. 2004-07-27. A surprising fact about D-modules in characteristic p>0. https://arxiv.org/abs/math/0407464

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