Consistent Kaluza-Klein Reductions for General Supersymmetric AdS Solutions

For the most general supersymmetric solutions of type IIB supergravity consisting of a warped product of AdS5 with a five-dimensional manifold M5, we construct an explicit consistent Kaluza-Klein reduction on M5 to minimal D = 5 gauged supergravity. Thus, any solution of the gauged supergravity can be uplifted on M5 to obtain an exact solution of type IIB supergravity. We also show that for general AdS4 × SE7 solutions, where SE7 is a seven-dimensional Sasaki-Einstein manifold, and for a general class of supersymmetric solutions that are a warped product of AdS4 with a seven-dimensional manifold N7, there is an analogous consistent reduction to minimal D = 4 gauged supergravity.