The ell-independence conjecture for unipotent fundamental groups

Let $X/F$ be a geometrically connected variety with a base point $x\in X(F)$, and let \pi_1^\u0**eell(X,x) be its ell-adic unipotent fundamental group viewed as a pro-unipotent representation of $W_F'$. Let $A_{\u0**eell,X,x}$, $L_{\u0**eell,X,x}$, and $\hat{\mathcal{U}}_{\u0**eell,X,x}$ denote its Hopf algebra, Lie algebra, and completed universal enveloping algebra. Unipotent fundamental-group ell-independence conjecture. The collection \{\pi_1^\u0**eell(X,x)\}_\u0**eell is ${\mathbb Q}$-compatible; equivalently, the corresponding collections of Hopf algebras, Lie algebras, and associative algebras are ${\mathbb Q}$-compatible. This is the strongest proposed form of ell-independence for fundamental groups, and its general validity remains open.