11 problems

Let $E$ be an elliptic curve defined over a number field. Supersingular-prime infinitude conjecture. The curve $E$ has infinitely many prime ideals of supersingular reduction. This…

Let $E$ be the elliptic curve over $K=\mathbb{Q}(i)$ given by … with $j_E=\frac{2^{14}}{i-4}$. Let $x$ tend to infinity and count the supersingular primes of $E$ up to $x$. Elkies'…

Let $A/\mathbb{Q}$ be an abelian surface, and let $\pi_{A,ss}(x)$ denote the number of primes $p\leq x$ at which the reduction $\overline{A}_p$ is supersingular. Assume that $A$ be…

Let $f=\sum_{n\geq 1}a_nq^n$ be a non-CM newform of weight $2$, level $N$, and Nebentypus character $\epsilon$, and let $A_f/\mathbb{Q}$ be the absolutely simple abelian variety at…

Let $F$ be a number field, and consider a non-CM modular form of weight at least $4$. A prime is supersingular when the corresponding Fourier coefficient vanishes. Lehmer's conject…

Let $f$ be a modular form in the setting above, let $\theta$ be a character of the torsion subgroup of the cyclotomic Galois group, and let $\operatorname{Col}^{\pm,\theta}$ be the…

Let $f$ be a normalised eigen-newform of weight $k\ge2$, let $p$ be supersingular for $f$, and let $\mathcal E$ be the elliptic curve corresponding to $f$ in the elliptic-curve cas…

Let $E$ be the elliptic curve and let $K_\infty$ be the cyclotomic extension in the paper. For a character $\eta:\Delta\rightarrow\mathbb{Z}_p^\times$, let…

Supersingular-prime congruence classification conjecture. Then $d\mid\alpha$, and both $d$ and $E$ are among those given in Theorem 1.3.

Finiteness and uniform-boundary conjecture. For every $\alpha\in\mathbb Z$, the sets $S(\alpha,\mathbb Q)$ and $O(\alpha,\mathbb Q)$ are finite, and there exists a real number…

Let $d$ and $\alpha$ be integers defining a pair $(d,\alpha)$ for the KKP question in its strong form. Earlier results show that the question has no solutions when…