Local cohomology and support for triangulated categories. (English, French summaries) Ann. Sci. Éc. Norm. Supér. (4) 41 (2008), no. 4, 573–619. The authors of this nice paper on the one hand propose a new method for defining a notion of support for objects in suitable triangulated categories, which unifies several related approaches in various contexts, and on the other hand using this method prove in a conceptual way several interesting results, many of them known only in special cases, while others are new in all relevant contexts. The working setting of the paper is that of a compactly generated triangulated category T equipped with a ring homomorphism R → Z(T) from a graded-commutative Noetherian ring R, considered as a ring of cohomology operations on T, to the graded center Z(T) of T. For any objects X, C in T, the Z-graded abelian group H ∗ ∐ C (X) = n∈Z HomT(C, X[n]), considered as the cohomology of X with respect to C, inherits a Z(T)-module structure and therefore an R-module structure. First the authors discuss some notions related to support for modules. Let Spec R be the set of graded prime ideals of R. The (cohomological) support suppRM of a (graded) R-modul
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