8 problems

Let $k$ be the field of constants, let $Y$ be a smooth algebraic variety over $k$, let $Z$ be a divisor in $Y$, and let $({\mathcal M},\nabla) \in {\bf MIC}((Y \setminus Z)/k)$. Fo…

Let $K$ be a complete discrete valued field with equal characteristic $0$, and let $\mathcal{X}$ be a uniruled variety over $K$. Say that a proper geometrically integral smooth $K$…

Let $K$ be a complete discrete valued field with equal characteristic $0$, and let $\mathcal{X}$ be a smooth proper integral variety of dimension $n$ over $K$. Write…

Berkovich approximation conjecture. Every nonlattice string in the Berkovich projective line can be approximated by lattice strings with increasingly large oscillatory periods.

Approximation conjecture. Every nonlattice string in the Berkovich projective line can be approximated by lattice strings with increasingly large oscillatory periods.

Let $k$ be a valued field, let $\mathfrak X$ be locally of the form $\operatorname{Spf}(\mathcal A^\circ)$ for $k$-affinoid algebras $\mathcal A$, so that $\mathfrak X$ is of finit…

Let $K'/K$ be a finite field extension, let $X'$ be a separated $K'$-scheme locally of finite type over $K'$, and let $(X')^\mathrm{an}$ be the associated $K'$-analytic Berkovich s…

Soient $K$ un corps de nombres, $A$ l'anneau de ses entiers et $\a0\Sigma_{\infty}$ l'ensemble des plongements de $K$ dans $\mathbf{C}$. Notons $A_{1^-}[[X]]$ le sous-anneau de…