10 problems

Let $K$ be the field and let $\Sigma$ be the index set used to define the spaces of multiple polylogarithms and multiple zeta values. Let … be the map obtained by composing the map…

Thakur's basis conjecture. The set $\mathcal{B}^{\mathrm{T}}_w$ is a basis of the $k$-vector space $\mathcal{Z}_w$.

Todd's dimension conjecture. For every positive integer $w$,

Let $k$ be the rational function field underlying the paper, let $v$ be a finite place of $k$, and let $\overline{\mathcal{Z}}$ and $\overline{\mathcal{Z}}_v$ denote the correspond…

Let $\overline{\mathfrak{Z}}$ be the $\overline{\mathbb{Q}}$-algebra generated by multizeta values, and let $\overline{\mathfrak{Z}}_w$ be the $\overline{\mathbb{Q}}$-vector space…

Let $L$ be a field finitely generated over an algebraically closed field $l_0$ of characteristic $p$, and let $C$ be an abelian variety over $L$. For each $\ell\geqslant 0$, choose…

Let $q=p^l>2$, let $1\leq p^m\leq q$, let $n>0$ and $r\geq 2$, and let $N_i\in \mathbb{N}\cup\{0\}$ for $0\leq i\leq n-1$ satisfy … If … then the displayed multizeta value below is…

For a multizeta value $\zeta_{A}(s_{1},\ldots,s_{r})$ of weight $w:=\sum_{i=1}^{r}s_i$, call it zeta-like if the ratio $\zeta_{A}(s_{1},\ldots,s_{r})/\zeta_{A}(w)$ is algebraic ove…

Let $p$ be a prime, let $f\in \overline{\mathbb{F}}_p(x)$ be a separable rational map, and let $\zeta(f,\mathbb{P}^1(\overline{\mathbb{F}}_p);t)$ denote its Artin–Mazur zeta functi…

Let $K_0$ be the function field of a smooth curve over a finite field ${\Bbb F}$ of characteristic $p$, let $K_0^{\rm s}$ be a separable closure of $K_0$, and let $B$ be an abelian…