Endpoint Strichartz estimates for the magnetic Schrödinger equation

We prove Strichartz estimates for the Schrödinger equation with an electromagnetic potential, in dimension n⩾3. The decay and regularity assumptions on the potentials are almost critical, i.e., close to the Coulomb case. In addition, we require repulsivity and a nontrapping condition, which are expressed as smallness of suitable components of the potentials, while the potentials themselves can be large. The proof is based on smoothing estimates and new Sobolev embeddings for spaces associated to magnetic potentials.