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arXiv · 1606.00536

On injective dimension of F-finite F-modules and holonomic D-modules

Wenliang Zhang
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Abstract

We investigate injective dimension of $F$-finite $F$-modules in characteristic $p$ and holonomic $D$-modules in characteristic 0. One of our main results is the following. If, either $R$ is a regular ring of finite type over an infinite field of characteristic $p>0$ and $M$ is an $F_R$-finite $F_R$-module, or $R=k[x_1,\dots,x_n]$ where $k$ is a field of characteristic 0 and $M$ is a holonomic $D(R,k)$-module, then the injective dimension of $M$ is the same as the dimension of its support.

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Wenliang Zhang. 2016-06-02. On injective dimension of F-finite F-modules and holonomic D-modules. https://doi.org/10.1112/blms.12050

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