2022/05/02 by Díaz, Lázaro O. Rodríguez
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2205.01032
We apply Ohi's criterion for faithfully flatness of extensions of commutative rings to prove that any étale extension k[Y1, …, Yn]⊆ k[X1, …, Xn] of polynomial rings (each in n indeterminates) over a commutative ring k is faithfully flat. In particular, if k is an algebraically closed field then any étale polynomial map kn → kn is surjective.