Geelen–Gerards–Whittle's matroid structure theorem

Let $\mathbb{F}$ be a finite field, and let $\mathcal{M}$ be a proper minor-closed class of $\mathbb{F}$-representable matroids. If $M \in \mathcal{M}$ is sufficiently large and has sufficiently high branch-width, then $M$ has a tree-decomposition whose parts correspond to mild modifications of matroids representable over a proper subfield of $\mathbb{F}$, or to mild modifications of frame matroids and their duals.

Matroid structure theorem. The stated tree-decomposition exists.

This is the matroid analogue of the Graph Minors Structure Theorem and is intended to describe highly connected matroids in proper minor-closed classes. The paper explains that the announced result is false and proposes weaker replacement conjectures, so this original formulation is refuted.