Injective dimension of \(D\)-modules: A characteristic-free approach
Let \(A\) be a ring of formal power series in a finite number of variables over a field \(k\), and \(M\) a module over the ring of \(k\)-linear differential operators on \(A\). Then the injective dimension of \(M\) in the category of \(A\)-modules is bounded from above by the dimension of the support of \(M\). A characteristic-free proof of this fact is given, and this is applied to give a characteristic-free proof for a similar result for local cohomology modules. This latter result was proved in characteristic \(p>0\) [\textit{C. I. Huneke} and \textit{R. Y. Sharp}, Trans. Am. Math. Soc. 339, No. 2, 765-779 (1993; Zbl 0785.13005); \textit{G. Lyubeznik}, J. Reine Angew. Math. 491, 65-130 (1997; Zbl 0904.13003)] and in characteristic 0 [\textit{G. Lyubeznik}, Invent. Math. 113, No. 1, 41-55 (1993; Zbl 0795.13004)] using totally different methods.
scientific article; zbMATH DE number 1474723