The homotopy category of flat modules, and Grothendieck duality

The homotopy category of flat modules, and Grothendieck duality

Let R be a ring. We prove that the homotopy category K ( R -Proj) is always -compactly generated, and, depending on the ring R , it may or may not be compactly generated. We use this to give a description of K ( R -Proj) as a quotient of K ( R -Flat). The remarkable fact is that this new description...

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Veröffentlicht in:Inventiones mathematicae 2008-11, Vol.174 (2), p.255-308
1. Verfasser: Neeman, Amnon
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description Let R be a ring. We prove that the homotopy category K ( R -Proj) is always -compactly generated, and, depending on the ring R , it may or may not be compactly generated. We use this to give a description of K ( R -Proj) as a quotient of K ( R -Flat). The remarkable fact is that this new description of K ( R -Proj) generalizes to non-affine schemes; this will appear in Murfet’s thesis.
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title The homotopy category of flat modules, and Grothendieck duality
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