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An Isaac Newton Institute Programme

Model Theory and Applications to Algebra and Analysis

Galois axioms for fields

23rd March 2005

Author: Koenigsmann, J (Freiburg)

Abstract

I will sketch the proof of a new result in birational anabelian geometry: Almost any perfect field K is determined up to isomorphism by the absolute Galois group of th rational function field K(t) over K. This gives rise to an axiomatization of the elementary theory of K by axiomatizing the complete system of finite quotients of this absolute Galois group. As application, I will indicate consequences for the decidability of the perfect hull of F_p((t)).