7 problems

Let $G$) be a smooth affine group scheme over ${\mathbb{Z}}/p^n{\mathbb{Z}}$ equipped with a 1-bounded cocharacter $\mu:{\mathbb{G}}_m\to G$. Let $\operatorname{BT}_n^{G,\mu}$ be t…

Drinfeld's extension conjecture. The isomorphism between these restrictions extends to an isomorphism over the whole $\operatorname{Disp}_1^G$.

Drinfeld's conjecture. The new stack is canonically isomorphic to the reduction modulo $p$ of the stack of $1$-truncated Barsotti–Tate groups of height $d$ and dimension $d'$.

Comparison-isomorphism conjecture. The morphism $\Upsilon^{\mathrm{sm}}$ is an isomorphism.

Bültel–Pappas conjecture. The functor

Fix a local unramified Shimura datum $(G,[b],\{\mu\})$, choose an integral representative $\mu$ and a representative $b$ such that $b=u\mu^\sigma(p)$, and let…

Let $G$ be the group in the local unramified Shimura datum, let $b$ be a representative of its $\sigma$-conjugacy class, and let $W$ be the Witt-vector ring used in the constructio…