6 problems

For $m\ge 1$, let $e_i$ denote the $i$-th elementary symmetric function in the variables used to define $f_m^{(1)}$. The closed formula conjecture for genus-one ramification polyno…

For $g=0$ and $m\ge 3$, or $g\ge 1$ and $m\ge 1$, let $f_m^{(g)}(\alpha_1,\ldots,\alpha_m)$ denote the rescaled ramification number associated with coverings of the sphere by a gen…

Let $m\ge 1$, let $\alpha=(\alpha_1,\ldots,\alpha_m)$ be a ramification type, and let $n=\alpha_1+\cdots+\alpha_m$. For $i=1,\ldots,m$, let $e_i$ be the $i$-th elementary symmetric…

General form conjecture. For every $g\ge2$,

Let $X$ be a smooth projective algebraic curve defined over an algebraically closed field $K$ of characteristic zero and transcendence degree $h$. A finite ramified covering…

Let $k(x)$ be the function field of the projective line, and let $E$ be a finite regular Galois extension of $k(x)$ with Galois group $G$. Equivalently, the inclusion…