Proposition of the day

Let X be a scheme. Let a : X —> Spec(k1) and b : X —> Spec(k2) be morphisms from X to spectra of fields. Assume a,b are locally of finite type, and X is reduced, and connected. Then we have k′1 = k′2, where k′i ⊂ Γ(X,OX) is the integral closure of ki in Γ(X,OX). See Tag 04MK.