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 AdS(5) with a five-dimensional manifold M-5, we construct an explicit consistent Kaluza-Klein reduction on M-5 to minimal D = 5 gauged supergravity. Thus, any solution of the gauged supergravity can be uplifted on M-5 to obtain an exact solution of type IIB supergravity. We also show that for general AdS(4) x 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 AdS(4) with a seven-dimensional manifold N-7, there is an analogous consistent reduction to minimal D = 4 gauged supergravity.