Algebraization conjecture for the formal group H_Σ

Let $H_\Sigma$ be the formal group over the stack $\Sigma$ introduced above. An algebraization of $H_\Sigma$ is an isomorphism class of a smooth affine group scheme over $\Sigma$ with connected fibers, together with an isomorphism from $H_\Sigma$ to its formal completion along the unit. Algebraization conjecture for $H_\Sigma$. Such an algebraization of $H_\Sigma$ exists. The preceding discussion constructs a canonical algebraization after pullback along $F:\Sigma\to\Sigma$ and shows that an algebraization of $H_\Sigma$, if it exists, is unique; existence is the remaining conjectural assertion.