Scale-invariant Strichartz estimates on tori and applications We prove scale-invariant Strichartz inequalities for the Schrödinger equation on rectangular tori (rational or irrational) in all dimensions. We use these estimates to give a simpler treatment of local well-posedness of the energy-critical nonlinear Schrödinger equation in dimensions three and four. 23 2 445-472 445-472 International Press