We prove global-in-time Strichartz estimates without loss of derivatives for the
solution of the Schrödinger equation on a class of nontrapping asymptotically conic
manifolds. We obtain estimates for the full set of admissible indices, including the
endpoint, in both the homogeneous and inhomogeneous cases. This result improves
on the results by Tao, Wunsch and the first author and by Mizutani, which are local
in time, as well as results of the second author, which are global in time but with a
loss of angular derivatives. In addition, the endpoint inhomogeneous estimate is a
strengthened version of the uniform Sobolev estimate recently proved by Guillarmou
and the first author. The second author has proved similar results for the wave
equation.