11 problems

Weak admissibility conjecture. The specialization map $\iota_{\widehat{F}}$ is an isomorphism, and

Let $X_\eta$ be the generic fibre of the strictly semi-stable scheme considered in the paper, let $\mathcal{E}^{\dagger}_K$ be the bounded Robba-ring coefficient field, and write…

Let $R$ be a complete discrete valuation ring with fraction field $K$ and finite residue field $k$ of characteristic $p$, and let $X$ be a proper flat scheme over…

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

Let $X\to S$ be proper, flat, generically smooth and regular. Let $\operatorname{sp}'$ be the specialization map from rigid cohomology to crystalline cohomology, and let $W_{i-1}$…

Let $X\to S$ be proper, flat and generically smooth, with special fibre $X_s$ over $k$ and geometric generic fibre $X_{\bar\eta}$. Let $H^i_{\operatorname{rig}}(X_s/k)$ be rigid co…

Let $X\to S\subseteq \mathbb A^1_{\mathbb F_q}\setminus\{0\}$ be a morphism of varieties over $\mathbb F_q$ with a good lift around $t=0$. Let…

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,…