The highlights of this chapter are Hopkins’ theorem on perfect complexes over commutative noetherian rings, which is the content of Section 2.1, and its analogue in modular representation theory, proved by Benson, Carlson, and Rickard; this appears in Section 2.3. This requires a discussion of appropriate notions of support; for commutative rings, this is based on the material from Appendix A, while for modules over group algebras, one requires more sophisticated tools, from homotopy theory, and these are discussed in Section 2.2.
KeywordsCommutative Ring Projective Resolution Localisation Functor Triangulate Category Koszul Complex
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