Coleman's conjecture on circular distributions

Let $\mathcal{F}^{\rm d}$ be the group of distributions, let $\mathcal{F}^{\rm c}$ be the $R$-submodule of strict distributions generated by the cyclotomic distribution $\Phi$, and let $\mathcal{D}$ be the $R$-submodule generated by the Coleman distributions $\delta_\Pi$ associated with non-empty sets $\Pi$ of odd primes. Coleman's conjecture.

$$\mathcal{F}^{\rm d}=\mathcal{D}+\mathcal{F}^{\rm c}.$$

The conjecture was later shown to be false because $\mathcal{F}^{\rm c}$ is torsion-free, whereas the torsion subgroup of $\mathcal{F}^{\rm d}$ has uncountably infinite dimension over $\mathbb{F}_2$; this motivates a corrected torsion-free formulation.