Definability problems regarding Campana points and Darmon points

Abstract: Campana points and Darmon points arise in algebraic geometry to generalize m-full integers and perfect m-th powers, respectively, to more arbitrary varieties. In this talk we will study the problem of defining these objects over number fields using first-order language, and we will conclude by building on a result by Fritz, Pasten, and Pheidas which shows that the diophantineness of Campana points on complex rational functions in one variable is incompatible with Kollar's conjecture, an argument that can be easily adapted for Darmon points as well. This will motivate further research on the analogous definability of these sets over C(z).

algebraic geometrylogicnumber theory

Audience: researchers in the topic

Online logic seminar

Series comments: Description: Seminar on all areas of logic