Restricted projections and Fourier decoupling in Qₚⁿ

We prove a restricted projection theorem for Borel subsets of Qₚⁿ in the regime p>n. This generalizes results of Gan-Guo-Wang in the real setting. Our result is effective in the sense that explicit constants are obtained for various covering numbers. Along the way, we prove a fully explicit Fourier decoupling theorem for the moment curve in p-adic Cartesian space.