A model theory section conjecture

TL;DR

This paper formulates aspects of Grothendieck's section conjecture within model theory, using stability theory to explore fundamental questions in anabelian geometry.

Contribution

It introduces a new categorical framework linking model theory and anabelian geometry, providing a novel perspective on the section conjecture.

Findings

Formulated a model-theoretic version of the section conjecture

Connected stability theory with problems in anabelian geometry

Provided a new categorical approach to interpret geometric conjectures

Abstract

We introduce the category of structures and interpretations which allows us to discuss some issues of Grothendieck's anabelian geometry in model-theory terms. Our main result is a formulation in terms of pure stability theory of a problem closely related to Grothendieck's section conjecture