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Generalised sheaf cohomology theories. (English) Zbl 1063.55004
Greenlees, J. P. C. (ed.), Axiomatic, enriched and motivic homotopy theory. Proceedings of the NATO Advanced Study Institute, Cambridge, UK, September 9--20, 2002. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-1833-9/hbk). NATO Science Series II: Mathematics, Physics and Chemistry 131, 29-68 (2004).
The paper is an expanded version of notes for a set of lectures given at the Isaac Newton Institute for Mathematical Sciences (September 23 and 24, 2002). Its aim is to present some of the basic features of the homotopy theory of simplicial presheaves and the stable homotopy theory of presheaves of spectra, by specifying their use in applications. The sections of this paper are the following: 1. Simplicial presheaves; 2. Presheaves of spectra; 3. Profinite groups; 4. Generalized Galois cohomology theory; 5. Thomason’s descent theorem. For the entire collection see [Zbl 1050.57001].

55N30Sheaf cohomology (algebraic topology)
55N20Generalized homology and cohomology theories (algebraic topology)
55N35Other homology theories (algebraic topology)
55P42Stable homotopy theory, spectra