On the support of relative $D$-modules

Robin van der Veer

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arXiv · 2102.09476

On the support of relative $D$-modules

Robin van der Veer

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Abstract

In this article we investigate the fibers of relative $D$-modules. In general we prove that there exists an open, Zariski dense subset of the vanishing set of the annihilator over which the fibers of a cyclic relative $D$-module are non-zero. Next we restrict our attention to relatively holonomic $D$-modules. For this class we prove that the fiber over every point in the vanishing set of the annihilator is non-zero. As a consequence we obtain new proofs of a conjecture of Budur which was recently proven by Budur, van der Veer, Wu and Zhou, as well as a new proof of a theorem of Maisonobe. Moreover, we also obtain a diagonal specialization result for Bernstein-Sato ideals.

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Robin van der Veer. 2021-02-16. On the support of relative $D$-modules. https://arxiv.org/abs/2102.09476

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