### Abstract

Let (R, m) be a Noetherian regular local ring of characteristic p > 0 and let I be a nonzero ideal of R. Let D(−) = Hom_{R}(−, E) be the Matlis dual functor, where E = E_{R}(R/m) is the injective hull of the residue field R/m. In this short note, we prove that if H^{i} _{I}(R) ≠ 0, then Supp_{R}(D(H_{i} ^{I}(R))) = Spec(R).

Original language | English (US) |
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Pages (from-to) | 3715-3720 |

Number of pages | 6 |

Journal | Proceedings of the American Mathematical Society |

Volume | 146 |

Issue number | 9 |

DOIs | |

State | Published - Jan 1 2018 |

### Keywords

- F-modules
- Local cohomology
- Matlis duality

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## Cite this

Lyubeznik, G., & Yildirim, T. (2018). On the matlis duals of local cohomology modules.

*Proceedings of the American Mathematical Society*,*146*(9), 3715-3720. https://doi.org/10.1090/proc/14038