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Constructing pseudo-algebraically closed fields

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Constructing pseudo-algebraically closed fields

A field K is called pseudo-algebraically closed (PAC) if every absolutely irreducible variety defined over K has a K-rational point. These fields were introduced by Ax in his characterization of pseudo-finite fields and have since become an important object of study in both model theory and field arithmetic. We will explain how the analysis of a PAC field often reduces to questions about the model theory of the absolute group and describe how these reductions combine with a graph-coding construction of Cherlin, van den Dries, and Macintyre together with to construct PAC fields with prescribed combinatorial properties.

- Séminaire Géométrie et théorie des modèles

Détails :

Orateur / Oratrice : Nick Ramsey
Date : 6 mars 2020
Horaire : 17h00 - 18h20
Lieu : ENS Salle W