This will be a presentation of a result in complex algebraic geometry. Let X be a smooth projective complex surface of general type without non-trivial globally holomorphic 2-forms on it. The Bloch-Srinivas result says that if the diagonal of X is balanced then any two points on X are rationally equivalent to each other. Joint with Gorchinskiy, we proved the following principle. Take two points P and Q on X, such that the transcendence degree of P (over a fixed subfield in complex numbers) is 2, and the transcendence degree of Q is 0. Then, if P is rationally equivalent to Q, then any two points are rationally equivalent to each other on X.
