Hyperbolicity and model complete fields

Abstract: Given $C$ a (quasi-projective) curve over $\mathbb{Q}$ with genus at least 2 and $C(\mathbb{Q})$ is empty, the class of fields $K$ of characteristic 0 such that $C(K)=\emptyset$ has a model companion CXF. Models of CXF have an interesting combination of properties and provide examples to answer various questions around model theory of fields, field arithmetic, and decidability.

It turns out the existence of model companion is related to several notions of hyperbolicity in algebraic geometry. In particular, with the assumptions of different notions of hyperbolicity on V, our results admit generalisation to varieties V of arbitrary dimension. This talk is based on joint work with Will Johnson and joint work with Michal Szachniewicz.

algebraic geometrylogic

Audience: researchers in the topic

Online logic seminar

Series comments: Description: Seminar on all areas of logic