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

Research output: Contribution to journal › Article › peer-review

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

Bibliographical note

Funding Information:
The first author gratefully acknowledges NSF support through grant DMS-1500264. The second author was supported by TÜBİTAK2214/A Grant Program: 1059B141501072. The results in this paper were obtained while the second author visited the School of Mathematics at the University of Minnesota. The second author would like to thank TÜBİTAK for their support and also all members of the Mathematics Department of the University of Minnesota for their hospitality. Both authors would like to thank the referee for valuable comments that have improved the exposition.

Funding Information:
Received by the editors July 3, 2017, and, in revised form, July 6, 2017 and November 27, 2017. 2010 Mathematics Subject Classification. Primary 13D45, 13H05. Key words and phrases. Local cohomology, Matlis duality, F-modules. The first author gratefully acknowledges NSF support through grant DMS-1500264. The second author was supported by TÜBİTAK 2214/A Grant Program: 1059B141501072.

Publisher Copyright:
© 2018 American Mathematical Society.

Keywords

F-modules
Local cohomology
Matlis duality

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title = "On the matlis duals of local cohomology modules",

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(−) = 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).",

keywords = "F-modules, Local cohomology, Matlis duality",

author = "Gennady Lyubeznik and Tuğba Yildirim",

note = "Funding Information: The first author gratefully acknowledges NSF support through grant DMS-1500264. The second author was supported by T{\"U}BİTAK2214/A Grant Program: 1059B141501072. The results in this paper were obtained while the second author visited the School of Mathematics at the University of Minnesota. The second author would like to thank T{\"U}BİTAK for their support and also all members of the Mathematics Department of the University of Minnesota for their hospitality. Both authors would like to thank the referee for valuable comments that have improved the exposition. Funding Information: Received by the editors July 3, 2017, and, in revised form, July 6, 2017 and November 27, 2017. 2010 Mathematics Subject Classification. Primary 13D45, 13H05. Key words and phrases. Local cohomology, Matlis duality, F-modules. The first author gratefully acknowledges NSF support through grant DMS-1500264. The second author was supported by T{\"U}BİTAK 2214/A Grant Program: 1059B141501072. Publisher Copyright: {\textcopyright} 2018 American Mathematical Society.",

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T1 - On the matlis duals of local cohomology modules

AU - Lyubeznik, Gennady

AU - Yildirim, Tuğba

N1 - Funding Information: The first author gratefully acknowledges NSF support through grant DMS-1500264. The second author was supported by TÜBİTAK2214/A Grant Program: 1059B141501072. The results in this paper were obtained while the second author visited the School of Mathematics at the University of Minnesota. The second author would like to thank TÜBİTAK for their support and also all members of the Mathematics Department of the University of Minnesota for their hospitality. Both authors would like to thank the referee for valuable comments that have improved the exposition. Funding Information: Received by the editors July 3, 2017, and, in revised form, July 6, 2017 and November 27, 2017. 2010 Mathematics Subject Classification. Primary 13D45, 13H05. Key words and phrases. Local cohomology, Matlis duality, F-modules. The first author gratefully acknowledges NSF support through grant DMS-1500264. The second author was supported by TÜBİTAK 2214/A Grant Program: 1059B141501072. Publisher Copyright: © 2018 American Mathematical Society.

PY - 2018

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N2 - 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).

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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ER -

On the matlis duals of local cohomology modules

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