The main goal of Wednesday’s lectures is to introduce and develop a theory of support for triangulated categories endowed with an action of a commutative ring. The reason for doing this is that the proofs of the main results, to be presented in Friday’s lectures, involve various triangulated categories (of modules over group algebras, and differential graded modules over differential graded rings) and one needs a notion of support applicable to each one of these contexts. In fact, what is required is a more fundamental construction, which underlies support, namely, local cohomology functors. This unifies and extends Grothendieck’s local cohomology for commutative rings  and the technology of Rickard functors for the stable module category, presented in Section 2.3.5.
KeywordsCommutative Ring Compact Object Triangulate Category Local Cohomology Homotopy Category
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