## Abstract

We give a characteristic-free proof of the fact that if A is a ring of formal power series in a finite number of variables over a field k and M is any module over the ring of k-linear differential operators of A, then in the category of A-modules, the injective dimension of M is bounded above by the dimension of the support of M. This is applied to give a characteristic-free proof of the same inequality between the injective dimension and the dimension of the support for local cohomology modules H^{iI}(R) where R is any regular Noetherian ring containing a field and I ⊂ R is any ideal. This result for local cohomology modules had been proven before in characteristic 0 and characteristic p > 0 by two methods that were completely different from each other.

Original language | English (US) |
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Pages (from-to) | 205-212 |

Number of pages | 8 |

Journal | Journal of Pure and Applied Algebra |

Volume | 149 |

Issue number | 2 |

DOIs | |

State | Published - May 26 2000 |

### Bibliographical note

Funding Information:E-mail address: [email protected] (G. Lyubeznik) 1Supported by the National Science Foundation.