A surprising fact about D-modules in characteristic p>0
Commutative Algebra
2007-05-23 v1 Algebraic Geometry
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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Cite
@article{arxiv.math/0407464,
title = {A surprising fact about D-modules in characteristic p>0},
author = {Josep Alvarez Montaner and Gennady Lyubeznik},
journal= {arXiv preprint arXiv:math/0407464},
year = {2007}
}
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8 pages