Sharp local smoothing estimates for curve averages

We prove sharp local smoothing estimates for curve averages in all dimensions. As a corollary, we prove the sharp $L^p$ boundedness of the helical maximal operator in ${\mathbb{R}}^4$, which was previously known only for ${\mathbb{R}}^2$ and ${\mathbb{R}}^3$. We also improve previously known results in higher dimensions. There are new ingredients in the proof: Fourier decay estimates and wave envelope estimates for nondegenerate curves in ${\mathbb{R}}^n$. As a byproduct, we prove Bochner-Riesz estimates for nondegenerate curves in all dimensions.