Generators of $D$–modules in positive characteristic

By Josep Alvarez-Montaner, Manuel Blickle, Gennady Lyubeznik. 2005

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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 DR|k be the ring of klinear 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 DR|k-modules.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c2ce31edc7bf3a69913e4095ea92f4c2fa8f0724

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In Computational Theory and Mathematics

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Citations in the corpus

F-thresholds of hypersurfaces (2007, methodology): “[ AMBL ] for a fast introduction) which states that the Frobenius functor induces an equivalence of the category of R–modules and De”