Matzat's conjecture on absolute differential Galois groups

Let $k$ be an algebraically closed field of characteristic zero and let $F$ be a one-variable function field over $k$, equipped with a non-trivial $k$-derivation.

Matzat's conjecture. The absolute differential Galois group of $F$ is the free proalgebraic group on a set of cardinality $|F|$.

This conjecture concerns the structure of the absolute differential Galois group for one-variable function fields and is a central problem in differential Galois theory. The paper's abstract states that the conjecture is proved in full generality.