For a smooth hypersurface $X\subset\mathbb{P}^n_k$, where $k$ is an algebraic closed field of charactersitc $p>0$. How to compute its algebraic de Rham cohomology explicitly? or equivalently its Hodge number?
PS：In characteristic $0$ case, one has Lefschetz hyperplane theorem,Hirzebruch-Riemann-Roch and Hodge theory.
