On the matlis duals of local cohomology modules

Gennady Lyubeznik; Tuğba Yildirim

doi:10.1090/proc/14038

On the matlis duals of local cohomology modules

Gennady Lyubeznik, Tuğba Yildirim

Mathematics

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3 Scopus citations

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 Hⁱ _I(R) ≠ 0, then Supp_R(D(H_i ^I(R))) = Spec(R).

Original language	English (US)
Pages (from-to)	3715-3720
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	146
Issue number	9
DOIs	https://doi.org/10.1090/proc/14038
State	Published - 2018

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Publisher Copyright:
© 2018 American Mathematical Society.

Keywords

F-modules
Local cohomology
Matlis duality

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AB - Let (R, m) be a Noetherian regular local ring of characteristic p > 0 and let I be a nonzero ideal of R. Let D(−) = HomR(−, E) be the Matlis dual functor, where E = ER(R/m) is the injective hull of the residue field R/m. In this short note, we prove that if Hi I(R) ≠ 0, then SuppR(D(Hi I(R))) = Spec(R).

KW - F-modules

KW - Local cohomology

KW - Matlis duality

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On the matlis duals of local cohomology modules

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