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arXiv · 1708.06481

A dichotomy for the injective dimension of $F$-finite $F$-modules and holonomic $D$-modules

Nicholas Switala·Wenliang Zhang
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Abstract

Let $M$ be either an $F$-finite $F$-module over a noetherian regular ring of characteristic $p > 0$ or a holonomic $D$-module over a formal power series ring over a field of characteristic zero. We prove that $\injdim_R M$ enjoys a dichotomy property: it has only two possible values, $\dim \Supp_R M - 1$ or $\dim \Supp_R M$.

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Nicholas Switala, Wenliang Zhang. 2017-08-22. A dichotomy for the injective dimension of $F$-finite $F$-modules and holonomic $D$-modules. https://arxiv.org/abs/1708.06481

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