Christian d'Elbée (University of Leeds) – On Chatzidakis’ expansion of 𝔽_p^alg

In this talk we will present a 1989 paper of Chatzidakis which consists in the following. In a field of characteristic $p>0$, the Artin-Shreier map $x \mapsto x^p-x$ is an additive homomorphism. Chatzidakis considers and solves the question of the existence of a cross section of the Artin-Shreier map which has a decidable theory, by describing a model-companion. Then she constructs an explicit model within the algebraic closure $𝔽_p^{\textrm{alg}}$ of the prime field. The construction is quite involved and has a gap, and we will propose a fix for that gap, which is joint work with Martin Hils.