Basic Adic Formalism

Let η be the generic point of X; we note that the constant sheaf F on X is equal to η∗F (i.e., the natural map F → η∗ηF is an isomorphism). This is because any E which is quasicompact and étale over X must also be normal and Noetherian, so the connected components of E are its irreducible components, with their generic points exactly the points of the fiber Eη. Hence we reduce to showing that the higher étale cohomology of η∗F vanishes.