Etale covers of affine spaces in positive characteristic

We prove that every projective, geometrically reduced scheme of dimension n over an infinite field k of positive characteristic admits a finite morphism over some finite radicial extension k' of k to projective n-space, etale away from the hyperplane H at infinity, which maps a chosen Weil divisor into H and a chosen smooth geometric point of X not on the divisor to some point not in H.