7 problems

Let $\mathcal{M}_{g,n}$ be the moduli space of smooth curves of genus $g$ with $n$ marked points. Polynomial point-count conjecture. The space $\mathcal{M}_{g,n}$ has polynomial po…

Aubry et al.'s point-count conjecture. If $1=w_0\leq w_1\leq w_2\leq\cdots\leq w_n$ and $\operatorname{lcm}(w_1,w_2,\ldots,w_n)\mid d$, then

Let $V_{32}$ be the double cover considered in the paper, and let $G_4=\langle\alpha_1,\alpha_2\rangle$. Write $[V_{32}/G_4]_p$ for the number of points of the quotient over…

Let $V_{32}$ be the double cover considered in the paper, and let $\alpha_1$ and $\alpha_2$ be the two involutions acting on it. Write $[V_{32}/\alpha_i]_p$ for the number of point…

Let $Q_3$ and $R_3$ be the quotient varieties associated with the involution $\iota_3$, and let $[Q_3]_p$ and $[R_3]_p$ denote their numbers of points over $\mathbb F_p$. Let $a_p$…

Let $Q_2$ be the double cover considered in the paper, and let $[Q_2]_p$ denote its number of points over $\mathbb F_p$. Let $b_p$ be the Hecke eigenvalue of the newform of weight…

Let $q$ be fixed, let $g$ be the genus of a curve over the finite field $\mathbb{F}_q$, and let $n$ be a possible number of rational points. Consider the fraction of curves of genu…