Let k be a field. If X is smooth over Spec(k) then the set {x∈X closed such that k⊂κ(x) is finite separable} is dense in X. See Tag 056U.

Let k be a field. If X is smooth over Spec(k) then the set {x∈X closed such that k⊂κ(x) is finite separable} is dense in X. See Tag 056U.