On the local cohomology and support for triangulated categories (Q654864)

Let \(R\) be a graded commutative Noetherian ring. The notion of \(R\)-linear triangulated category \(\mathcal T\) is introduced in this paper. To each object \(X\) of \(\mathcal T\) a new subset of \(\text{Spect}(R)\), the big support of \(X\), is defined. The properties of this support is investigated in several situations following the ideas laid in the work of \textit{D. Benson}, \textit{S. Iyengar} and \textit{H. Krause} [Ann. Sci. Éc. Norm. Supér. (4) 41, No. 4, 575--621 (2008; Zbl 1171.18007)]. This study, specializing to categories generated by only one compact object led to a satisfactory theory of local cohomology for certain triangulated categories.