Étale Cohomology Seminar Lecture 2


Proposition 1.1. (a) Any open immersion is étale. (b) The composite of two étale morphisms is étale. (c) Any base change of an étale morphism is étale. (d) If φ ◦ ψ and φ are étale, then so is ψ. Proposition 1.2. Let f : X → Y be an étale morphism. (a) For all x ∈ X, OX,x and OY,f(x) have the same Krull dimension. (b) The morphism f is quasi-finite. (c) The… (More)