8 problems

Uniformity conjecture prediction. The answer to this question should be $\ell=2$. This prediction is conditional on the uniformity conjecture and is obtained by considering the dis…

Let $C/\mathbb{Q}(\zeta_m)$ be a superelliptic curve $y^m=f(x)$ as in the paper, let $\tau$ be a character of $C_m$, and fix an embedding…

Let $A=\mathbb{C}[x^{\pm1},u\mid u^2=P(x)]$, where $P(x)\in\mathbb{C}[x]$ is palindromic of even degree $2r$ with simple roots. Let $A/\partial A$ denote the quotient by exact deri…

Gerritzen–van der Put's conjecture. With this setup, the $(2g+2)$-element subsets $S \subset \mathbb{P}_K^1$ and $\mathcal{B} \subset \mathbb{P}_K^1$ have the same position.

Let $n=2\ell$, assume that the characteristic of $F$ is zero or sufficiently positive, and let $P^{\ell,*}_m$ be the atomic inflection polynomial of the Weierstrass pencil…

Let $F$ be the base field, let $n\geq 2$, and let $a,b,c$ be positive integers. Let $\mathcal{C}^{\ell}_m$ be the inflectionary curve derived from the pencil…

Superelliptic Jacobian group-isomorphism conjecture. There exists an isomorphism of abstract groups

Let $n$ be a non-prime integer, and consider the realizability result for tropical superelliptic curves established in the preceding theorem for prime integers $n$. Realizability c…