8 problems

Let ${\mathbf{k}}$ be an algebraically closed field of characteristic $0$, let $X=\mathcal{M}(A)$ be the affinoid space under consideration, and let $f:X\to X$ be an automorphism w…

Let ${\mathbf{k}}$ be a field of characteristic $0$, let $X=\mathcal{M}(A)$ be a ${\mathbf{k}}$-affinoid space, and let $f:X\to X$ be an automorphism. Analytic dynamical Mordell–La…

Green $\delta$-form conjecture. The form $\gamma$ is a Green $\delta$-form for $Z\setminus\partial Z$ on $X\setminus\partial X$. This would extend the stated complete-intersection…

Let $A,A_1,A_2,A_{12}$ be noetherian $\mathbb{E}_1$-Banach rings in the indicated simplicial ind-Banach categories. Suppose that their homotopy rings fit into a short strictly exac…

Tropicalization surjectivity conjecture. The map $\operatorname{Trop}$ is surjective. Moreover, if $g=\lvert\bm{\mu}\rvert$, then it is a bijection.

Cycle-class image conjecture. The image of $\operatorname{CH}(X)_\mathbb{Q}$ is

Liu's conjecture. The iterated monodromy operator above is an isomorphism for all $p\geq q$.

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…