11 problems

For each $n\in\mathbb{Z}_{>0}$, there should exist a prime $p$ such that, for every integer $m$ with $1\leq m\leq n$, there is a supersingular elliptic curve $E$ defined over…

Let $\mathcal{E}$ be the set of isomorphism classes of supersingular elliptic curves defined over $\overline{\mathbb{F}}_p$ for all primes $p$, and let…

Let $A_\ell$ denote the weighted adjacency matrix of the supersingular $\ell$-isogeny graph $\mathcal{G}(p,\ell)$ for all $\ell\neq p$. Let $v$ be an $L^2$-normalized simultaneous…

Maximal-order containment conjecture. For every $\epsilon>0$, the number of maximal orders containing $\Lambda$ is

Let $F_f$ be a height $2$ and self-dual formal group, and let $\mathbb{U}'$ and $\mathbb{X}'$ be the torsion $\Lambda(G_{\infty},\mathcal{O}_{L_p})$-modules occurring in the paper.…

Let $E$ be an elliptic curve over $\mathds{Q}$ with good supersingular reduction at $p$ and $a_p=0$. Let $F$ be an imaginary quadratic field in which $p$ splits completely, let…

Let $E$ be an elliptic curve of prime conductor $p$ with root number $1$ and positive rank. Let $v_E=\sum v_E(e_i)e_i$ be the normalized eigenvector associated with $E$ in the Pica…

Chevyrev–Galbraith's linear-bound conjecture. In particular, they conjecture that

Let $p$ be a prime and let $B_p$ be the quaternion algebra over $\mathbb{Q}$ ramified precisely at $p$ and $\infty$. Let $\mathcal{O}$ and $\mathcal{O}'$ be maximal orders of $B_p$…

Let $p$ be the prime defining the quaternion algebra $B_p$, and let $\mathcal{O},\mathcal{O}'\subset B_p$ be maximal orders of different types. For an integer $b>0$, say that…

Let $p$ be the prime defining the quaternion algebra $B_p$, and let $\mathcal{O},\mathcal{O}'\subset B_p$ be maximal orders of different types. For an integer $b>0$, say that…