13 problems

For $d\neq 0,\pm3$, let $C_d$ be the genus-$2$ curve in the paper's displayed family, and let $g_d$ denote its analytic rank. Let $S(X)$ be the set of positive square-free integers…

Realization conjecture. All 54 reduction types of the genus $2$ classification are realised over $\mathbb{Q}$.

Let $C$ be a genus-$2$ curve, let $X_0$ be the relevant moduli space, and let ${\rm Wob}_0$ be its wobbly locus. Consider the construction using the spectral covering…

Good-extension path conjecture. For every two vertices $A$ and $A'$ in $\mathcal{J}_p\subsetmathcal{G}_p$, such a path exists.

Jacobian-subgraph connectedness conjecture. The subgraph of $\mathcal{G}_p$ supported on $\mathcal{J}_p$ is connected.

Let $\lambda_n$ be the integer sequence considered in Theorem, and let $\mathfrak{F}$ be the divisor chosen on the genus-2 curve ${\mathcal H}:y^2=x^5+10$, namely…

Prime-order conjecture for curve points. Define

For a prime $p>2$, let $P_1(p)$ be the probability that a uniformly randomly chosen integer in the Hasse–Weil interval $[(\sqrt p-1)^4,(\sqrt p+1)^4]$ is prime, and let $P_2(p)$ be…

For a prime $p>2$, let $P_1(p)$ be the probability that a uniformly randomly chosen integer in the Hasse–Weil interval $[(\sqrt p-1)^4,(\sqrt p+1)^4]$ is prime. Let $P_2(p)$ be the…

Let ${\mathcal C}_N$ be the family of genus-$2$ curves defined by integral binary sextics with coefficients bounded in absolute value by $N$. Stoll's logarithmic point-count conjec…

Let ${\mathcal C}_N$ be the family of genus-$2$ curves defined by integral binary sextics with coefficients bounded in absolute value by $N$. For a rational point $P$ on such a cur…

Let ${\mathcal C}_N$ be the family of genus-$2$ curves defined by integral binary sextics with coefficients bounded in absolute value by $N$. For a rational point $P=(a:y:b)$ with…

For $N>0$, let ${\mathcal C}_N$ be the set of genus-$2$ curves … with integral coefficients satisfying $|f_j|\leq N$ for all $j$, considered in the weighted projective plane with w…