On the Behavior of F-Rational Rings under Flat Base Change

We examine the behavior of F-rationality under flat homomorphisms with geometrically F-rational fibres. The goal is to prove that if R → S is a homomorphism with geometrically F-rational fibres and R is an F-rational ring, then S is an F-rational ring. We prove a stronger version of this under a mild condition and introduce a new perspective for dealing with flat base change problems in tight closure theory.