4 problems

Bhatt–Lurie’s conjecture. The class $\alpha_{{\mathrm F}}({\mathfrak X}_0)$ is the obstruction class for lifting ${\mathrm F}_{{\mathfrak X}_0}$ over $\phi_A:A_1\to A_1$.

Let $K$ be an imaginary quadratic field, let $p$ split in $K$, and let $\tau$ be the two-dimensional representation of $G_K$ inducing the representation under consideration. An inf…

The C-group Hodge–Tate conjecture. Then

The Hodge–Tate cocharacter conjecture. The element $\lambda_\sigma$ is the Hodge--Tate cocharacter associated to the embedding $F_v\to\overline{\mathbb{Q}}_p$.