Annihilators of D-modules in mixed characteristic

2019/07/23 by Datta, Rankeya, Switala, Nicholas, Zhang, Wenliang
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1907.09948

Abstract

Let R be a polynomial or formal power series ring with coefficients in a DVR V of mixed characteristic with a uniformizer π. We prove that the R-module annihilator of any nonzero \D(R,V)-module is either zero or is generated by a power of π. In contrast to the equicharacteristic case, nonzero annihilators can occur; we give an example of a top local cohomology module of the ring ℤ₂[[x₀, …, x₅]] that is annihilated by 2, thereby answering a question of Hochster in the negative.

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