All Questions

Conjecturally, there exists an integer $n$ such that the number of rational points of a genus $2$ curve over $\mathbf{Q}$ is at most $n$. (This follows from the Bombieri-Lang conjecture.) We are ...

We think the following is true: For all sufficiently large primes $p$ and all natural $g \ge 1$, there exists affine plane curve $f(x,y)=0$ over $\mathbb{F}_p$ which is non-singular, absolutely ...