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.

The main new ingredient is a novel wave envelope estimate adapted to moment curves, which is a powerful tool in the proof of the local smoothing estimate.