In the first section of the paper "Reconstruction of a variety from the derived category and groups of autoequivalences" of Bondal-Orlov (arXiv:alg-geom/9712029), the "well-known Brown lemma" is referenced several times with the paper "Cohomology theories" of E.H. Brown cited. I have heard of the Brown representability theorem which was proved in this paper, but I don't think this is the result being referenced by B-O. Does anyone know which lemma is being referred to?
A well-known lemma of Brown?
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algebraic-geometry
category-theory
triangulated-categories
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1I haven't checked it thoroughly, but I think they are referring to the ideas in section 3 of Brown's paper. Since they seem to provide the necessary ideas to complete the proofs of the relevant propositions 1.2 and 1.3, I think this reference is more an attribution of ideas than a suggestion that you should go and look into Brown's paper for proofs. – 2012-11-12
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0Commenter: thanks, I thought that might be the case. Is there any chance you know where one might be able to find the proofs (or at least the formal statements)? – 2012-11-13
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1Maybe section 8 of Keller's [Derived categories and their uses](http://www.math.jussieu.fr/~keller/publ/dcu.pdf) for contains the statements you're after, but I'm not sure if this is exactly what you're looking for. Some of the proofs appear in section 6 of Keller's [Derived categories and universal problems](http://www.math.jussieu.fr/~keller/publ/dcp.pdf) (lemmas 6.5 - 6.7). – 2012-11-13