# Jinhe Ye (Oxford)

Dates: | 10 May 2023 |
---|---|

Times: | 15:15 - 16:15 |

What is it: | Seminar |

Organiser: | Department of Mathematics |

Who is it for: | University staff, External researchers, Adults, Alumni, Current University students |

Title: Curve-excluding fields.

Abstract: Given $C$ a 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, which we call CXF. Models of CXF have interesting combinations of properties. For example, they provide an example of a model-complete field with unbounded Galois group, answering a question of Macintyre negatively. One can also construct a model of it with a decidable first-order theory that is not "large'' in the sense of Pop. Algebraically, it provides a field that is algebraically bounded but not ``very slim'' in the sense of Junker and Koenigsmann. Model theoretically, we find a pure field that is strictly $NSOP_4$.