On the injective dimension of $\mathscr{F}$-finite modules and holonomic $\mathscr{D}$-modules
| Autor: | Mehdi Dorreh |
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| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | Illinois J. Math. 60, no. 3-4 (2016), 819-831 |
| ISSN: | 0019-2082 |
| DOI: | 10.1215/ijm/1506067293 |
| Popis: | Let $R$ be a regular local ring containing a field $k$ of characteristic $p$ and $M$ be an $\mathscr{F}$-finite module. In this paper, we study the injective dimension of $M$. We prove that $\operatorname{dim}_{R}(M)-1\leq\operatorname{inj.dim}_{R}(M)$. If $R=k[[x_{1},\ldots,x_{n}]]$ where $k$ is a field of characteristic $0$ we prove the analogous result for a class of holonomic $\mathscr{D}$-modules which contains local cohomology modules. |
| Databáze: | OpenAIRE |
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