Open Access
Winter 2011 On the local cohomology and support for triangulated categories
Javad Asadollahi, Shokrollah Salarian, Reza Sazeedeh
Kyoto J. Math. 51(4): 811-829 (Winter 2011). DOI: 10.1215/21562261-1424866


Recently a notion of support and a construction of local cohomology functors for [TR5] compactly generated triangulated categories were introduced and studied by Benson, Iyengar, and Krause. Following their idea, we assign to any object of the category a new subset of Spec(R), again called the (big) support. We study this support and show that it satisfies axioms such as exactness, orthogonality, and separation. Using this support, we study the behavior of the local cohomology functors and show that these triangulated functors respect boundedness. Then we restrict our study to the categories generated by only one compact object. This condition enables us to get some nice results. Our results show that one can get a satisfactory version of the local cohomology theory in the setting of triangulated categories, compatible with the known results for the local cohomology for complexes of modules.


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Javad Asadollahi. Shokrollah Salarian. Reza Sazeedeh. "On the local cohomology and support for triangulated categories." Kyoto J. Math. 51 (4) 811 - 829, Winter 2011.


Published: Winter 2011
First available in Project Euclid: 10 November 2011

zbMATH: 1254.18009
MathSciNet: MR2854153
Digital Object Identifier: 10.1215/21562261-1424866

Primary: 13D45 , 18E30 , 18E35
Secondary: 16E40

Rights: Copyright © 2011 Kyoto University

Vol.51 • No. 4 • Winter 2011
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