Parametrization of Curves in Characteristic p

Let K be a complete ultrametric algebraically closed field of characteristic p.By applying the Nevanlinna Theory in characteristic p, we show that many algebraic curves admit no parametrizations by meromorphic functions in K, or by unbounded meromorphic functions inside an open disk, like it was shown in zero characteristic, provided we assume one of the function to have a non zero derivative.More generally, certain functional equations have no solution.In zero characteristic, results previously obtained are somewhat generalized, and then are extended to any characteristic.About functional equations f m + g n = 1, conclusions also are similar to those obtained in zero characteristic, provided we replace m, n by m = m|m| p , = n|n| p .