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For the most general supersymmetric solutions of type IIB supergravityconsisting of a warped product of AdS_5 with a five-dimensional manifold M_5,we construct an explicit consistent Kaluza-Klein reduction on M_5 to minimalD=5 gauged supergravity. Thus, any solution of the gauged supergravity can beuplifted on M_5 to obtain an exact solution of type IIB supergravity. We alsoshow that for general AdS_4 x SE_7 solutions, where SE_7 is a seven-dimensionalSasaki-Einstein manifold, and for a general class of supersymmetric solutionsthat are a warped product of AdS_4 with a seven-dimensional manifold N_7, thereis an analogous consistent reduction to minimal D=4 gauged supergravity.

Consistent Kaluza-Klein Reductions for General Supersymmetric AdS Solutions