The Cremona conjecture, also called Jacobi problem, claims that a polynomial morphism {{mathbb C}^n longrightarrow {mathbb C}^n} is invertible as a polynomial morphism if its Jacobian is constant and not zero. In this paper, we show that the conjecture is true for n = 2. The starting point of our proof is an important result of Shreeram Abhyankar. Then we use a computation in rigid geometry to achieve the result.