8 problems

A uniformizable abelian $t$-module with everywhere good reduction is an abelian $t$-module satisfying the stated uniformizability and reduction hypotheses. Its Lie algebra contains…

Let $\phi$ and $\psi$ be two almost strictly pure $t$-modules over $K$, and let $\phi\otimes\psi$ denote their tensor product. Choose a $K\{\tau\}$-basis of the corresponding $t$-m…

Cartier--Nishi duality conjecture. The Cartier--Nishi theorem holds for $\Upsilon$.

Double-duality and exact-sequence conjecture. For every triangular $\mathbf{t}$-module $\Upsilon$,

Let $K={\mathbb F}_q(\theta)$, let $F$ be a finite extension of $K$, let ${\cal O}_F$ be an integral closure of $A$ in $F$, and let $F_{\infty}=F\otimes_K K_{\infty}$. Let…

Let $K$ be the global function field in the setup, let $F\in\operatorname{End}_{\mathbb{F}_p}(\mathbb{G}_{a/K}^d)$ be an additive polynomial mapping, and let $\kappa$ and $\delta$…

Let $\mathcal{A}=(\mathbb{G}_{a}^{m},\Phi)$ be a uniformizable $T$-module such that there exists $i\in\mathbb{N}\setminus\{0\}$ for which the leading coefficient matrix of…

Let $\mathcal{A}=(\mathbb{G}_{a}^{m},\Phi)$ be a uniformizable $T$-module of dimension $m>1$ such that there exists $i\in\mathbb{N}\setminus\{0\}$ for which the leading coefficient…