5 problems

Let $f$ be a non-exceptional polynomial of degree $d\ge 2$. Let $Z\subset \mathbb{D}_R^n\times U_\infty(f)^n$ be an analytic subset of dimension $0\le m\le n$ defined by the parame…

Let $f$ be a non-exceptional polynomial of degree $d\ge 2$. Let $V_1\subset \mathbb{C}^n$ be an irreducible subvariety with non-empty intersection with $\mathbb{D}_R^n$, and let…

Salerno and Silverman's conjecture. The radius of convergence of $\phi^{-1}(x)$ in $\mathbb{C}_{p}$ is

Let $p$ be a prime and let $r\ge0$. Define … and let … be the associated Böttcher coordinate. Asymptotic valuation and radius conjecture. For $k\equiv0\pmod p$, … Moreover, the rad…

Let $p$ be a prime and let … Write the Böttcher coordinate of $\varphi$ as … where the coefficients $a_k$ are integers. Coefficient congruence conjecture. The following congruences…