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Recently a construction of local cohomology functors for compactly generated triangulated categories admitting small coproducts is introduced and studied by Benson, Iyengar, Krause, Asadollahi and their coauthors. Following their idea, we introduce the depth of objects in such triangulated categories and get that when $(R,\mathfrak{m})$ is a graded-commutative Noetherian local ring, the depth of every cohomologically bounded and cohomologically finite object is not larger than its dimension.
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참고문헌 (12)
참고문헌 신청
J. Asadollahi / 2011 / On the local cohomology and support for triangulated categories / Kyoto J. Math 51(4):811~829
L. L. Avramov / 2007 / Constructing modules with prescribed cohomological support / Illinois J. Math 51(1):1~20
D. J. Benson / 2008 / Local cohomology and support for triangulated categories / Ann. Sci. Ec. Norm. Super 41(4):573~619
D. J. Benson / 2012 / Colocalizing subcategories and cosupport / J. Reine Angew. Math 673:161~207
M. Brodmann / 1998 / Local cohomology: an algebraic introduction with geo-metric applications / Cambridge University Press
L. L. Avramov / 2007 / Constructing modules with prescribed cohomological support / Illinois J. Math 51(1):1~20
D. J. Benson / 2008 / Local cohomology and support for triangulated categories / Ann. Sci. Ec. Norm. Super 41(4):573~619
D. J. Benson / 2012 / Colocalizing subcategories and cosupport / J. Reine Angew. Math 673:161~207
M. Brodmann / 1998 / Local cohomology: an algebraic introduction with geo-metric applications / Cambridge University Press
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