# On function field Mordell-Lang: the semiabelian case and the socle theorem

## TL;DR

This paper advances the model-theoretic understanding of the function field Mordell-Lang conjecture by reducing the semiabelian case to the abelian case without relying on Zariski geometry dichotomies.

## Contribution

It provides a model-theoretic reduction from the semiabelian to the abelian case in the function field Mordell-Lang conjecture, extending previous results.

## Key findings

- Reduced semiabelian case to abelian case using model theory
- Avoided reliance on Zariski geometry dichotomy theorems
- Enhanced understanding of the conjecture's structure

## Abstract

We here aim to complete our model-theoretic account of the function field Mordell-Lang conjecture, avoiding appeal to dichotomy theorems for Zariski geometries, where we now consider the general case of semiabelian varieties. The main result is a reduction, using model-theoretic tools, of the semiabelian case to the abelian case.