2 problems

Darmon-Greenberg-Liu reciprocity conjecture. The extension $E_\tau(j)/E_\tau$ is conjectured to be an abelian extension unramified outside $2$. This is the concise field-theoretic…

Darmon-Greenberg-Liu algebraicity conjecture. The number $j$, which a priori belongs to $\mathbb{C}_p$, is algebraic for every special point $x\in X_p$ of the type described above.…