We prove that the theory of fields with a derivation of Frobenius has the model companion which is stable and admits elimination of quantifiers up to the level of the λ-functions. Along the way, we give new geometric axioms of DCFp.
"Derivations of the Frobenius map." J. Symbolic Logic 70 (1) 99 - 110, March 2005. https://doi.org/10.2178/jsl/1107298512