6 problems

Let $D$ be a $p$-divisible group, with codimension $c$ and dimension $d$. Its isomorphism number $n_D$ is the smallest non-negative integer such that, for every $p$-divisible group…

Let $k$ be a field of characteristic $p>0$, and let an overconvergent $(F,\nabla)$-crystal over $k((t))$ be given. A crystal is potentially semistable if it becomes semistable afte…

Let $k((t))$ be a local function field and let an overconvergent $(F,\nabla)$-crystal over $k((t))$ be given. A crystal is potentially semistable if, after a finite extension…

Let $p$ be a prime, let $X$ be a separated finite-type scheme over $\mathbb{F}_p$, and let $\mathcal{L}$ be a lisse $\mathbb{Z}_p$-sheaf with associated unit $F$-crystal…

Let $f$ be a homogeneous polynomial defining a smooth hypersurface family, and let $\alpha_s$ be the matrices associated with the Laurent polynomial construction, with $\sigma$ the…

Let $\Bbbk$ be an algebraically closed field of characteristic $p>0$, and let $D$ be a $p$-divisible group over $\Bbbk$. Its isomorphism number $n_D$ is the smallest nonnegative in…