11 problems

Let $Y_0$ be a $k$-scheme, let $X_0$ be a smooth ambient scheme when specified, and let $\rho_{Y_0,X_0}:\mathrm{Isoc}^{\dag}(Y_0/K)\to\mathrm{Isoc}^{\dag}(Y_0,X_0/K)$ and…

Let $I$ be an index set, let $X_i$ be the varieties equipped with partial Frobenius actions, and let $X/\Phi$ be the associated partial Frobenius stack. Write…

Caro's conjecture. The functor

Stronger Shiho conjecture. There exists a unique overconvergent $(F)$-isocrystal $\widetilde E$ on $(S,\overline{S})$ such that

Shiho's conjecture. There exists a unique overconvergent $(F)$-isocrystal $\widetilde E$ on $(S,\overline{S})$ whose restriction to…

Tsuzuki's conjecture. There is a unique object

Berthelot's conjecture. There is a unique object

Equivalence conjecture. There is a canonical equivalence of categories

Canonical equivalence conjecture. The canonical functor

Let $k$ be the perfect field and $\mathcal{S}$ the fixed formal base. Let $X$ be a smooth separated $k$-scheme of finite type, and let $X\hookrightarrow\overline{X}$ be an open imm…

Let $(S,S,\mathcal{S})$ be a triple endowed with a lift of Frobenius on $\mathcal{S}$, and let … be a diagram of pairs such that $f:\overline{X}\to\overline{Y}$ is proper,…