Derived Reid's recipe for abelian subgroups of SL3(C)

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For any finite subgroup G in SL3(C), work of Bridgeland-King-Reid constructs an equivalence between the G-equivariant derived category of C³ and the derived category of the crepant resolution Y = G-Hilb(C³) of C³/G. When G is abelian we show that this equivalence gives a natural correspondence between irreducible representations of G and certain sheaves on exceptional subvarieties of Y, thereby extending the McKay correspondence from two to three dimensions. This categorifies Reid's recipe and extends earlier work from [CL09] and [Log10] which dealt only with the case when C³/G has one isolated singularity.