4 problems

Asymptotic exponent conjecture. The detailed asymptotic behavior is

Graphical-extension conjecture. The graphical approach employed in the proof of the formula for $\nu(N-3,N)$ can be extended to other cases beyond the cases $K=N-1$, $K=N-2$, and…

For a finite field $\mathbb F_q$, let $F$ be a random element of the coset $\operatorname{GSp}^{(q)}_{2g}(\mathbb Z_\ell)$ of symplectic similitudes with similitude factor $q$, and…

Let $C$ be a smooth projective curve over $\mathbb F_q$, let $S\subset C$ be a reduced effective divisor, and consider smooth projective double covers $D\to C$ unramified over $S$.…