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).
Bibliographical noteFunding 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.
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.
© 2018 American Mathematical Society.
- Local cohomology
- Matlis duality