A Note on the Axioms for Differentially Closed Fields of Characteristic Zero

We rework the foundations of the theory of differentially closed fields of characteristic zero in a geometric setting. The “new” axioms will say that ifVis an irreducible variety andWis an irreducible subvariety of the appropriate torsor τ(V) projecting generically ontoV, thenWhas a generic point of the form (a, D(a)).