Power Series and p-Adic Algebraic Closures Original Research Article

We describe a presentation of the completion of the algebraic closure of the ring of Witt vectors of an algebraically closed field of characteristic p>0. The construction uses “generalized power series in p” as constructed by Poonen, based on an example of Lampert, and also makes use of an analogous construction of the algebraic closure of a field of power series in positive characteristic.