Frrom the text: For a field \(K\) of characteristic 0 and a complete discrete valuation ring \(A\) containing \(K\), the authors show that \(A\) is isomorphic to the ring of formal power series \(K_0[[X]]\) over some field \(K_0\). If moreover \(K\) is algebraically closed, and \(A\) is a field (i.e., \(A\) is a complete discrete valued field), it is shown that \(A\) is isomorphic to the field of formal Laurent series \(K_0((X))\) over some field \(K_0\).