10 problems

Let $k$ be a field, let $Y$ be a separated smooth $k$-scheme, let $E$ be an overconvergent $F$-isocrystal on $Y$, and let $\mathrm{sp}_{Y+}(E)$ denote its specialization. An arithm…

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 $\Psi$ be the nearby-cycle object with filtrations $F$ and $G$, let $\mathbb{D}$ denote duality, and let $b$ be the isomorphism relating the dual nearby cycles to…

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 $S$ be the base formal scheme, let $\eta$ denote its generic point, and let $\mathbb{D}_S$ and $\mathbb{D}_{\mathfrak{S}}$ be the corresponding arithmetic differential-operator…

Let $X$ be a smooth proper curve over $\mathbb{F}_p$, let $G\to X$ satisfy the stated hypotheses, and let $\mathcal{E}\in\mathbb{D}_{\mathrm{hol}}(X)$ be an augmented commutative…

Finite-dimensionality conjecture. Its cohomology

Let $X$ be a smooth proper curve over $\mathbb{F}_p$, let $G\to X$ satisfy the stated smoothness, affine, semisimplicity, simple-connectedness, and connected-fiber hypotheses, and…

Caro's conjecture. The functor

Let ${\mathcal X}$ be a smooth formal scheme, let $Z$ be a divisor of its special fibre, and write ${\mathcal U}$ for the complement of $Z$. Let ${\mathcal E}^\dagger$ be a coheren…