Puiseux Expansions in Nonzero Characteristic

Sanju Vaidya

A chapter in Algebra, Arithmetic and Geometry with Applications, 2004, pp 767-774 from Springer

Abstract: Abstract Let k be an algebraically closed field of characteristic p and let X be an indeterminate. Let k((X)) be the quotient field of the ring of formal power series (no convergence involved) in X over the field k. The field k((X)) is called the field of meromorphic functions of X over k. It is well known that in case p = 0, then the Puiseux field $$ \cup _{n = 1}^\infty k((X^{\tfrac{1} {n}} )) $$ of all Puiseux expansions is an algebraic closure of the field k((X)). But if p ≠ 0, this is not the case. In Chevalley [2], he proved that the polynomial Z p - Z - X -1 does not have a root in the Puiseux field.

Date: 2004
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DOI: 10.1007/978-3-642-18487-1_47

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