  Geelen, Gerards, and Whittle [3] announced the following result: let $q =
p^k$ be a prime power, and let $\mathcal{M}$ be a proper minor-closed class of
$\mathrm{GF}(q)$-representable matroids, which does not contain
$\mathrm{PG}(r-1,p)$ for sufficiently high $r$. There exist integers $k, t$
such that every vertically $k$-connected matroid in $\mathcal{M}$ is a
rank-$(\leq t)$ perturbation of a frame matroid or the dual of a frame matroid
over $\mathrm{GF}(q)$. They further announced a characterization of the
perturbations through the introduction of subfield templates and frame
templates.
  We show a family of dyadic matroids that form a counterexample to this
result. We offer several weaker conjectures to replace the ones in [3], discuss
consequences for some published papers, and discuss the impact of these new
conjectures on the structure of frame templates.
