4 problems

Let $X$ be a smooth, projective, geometrically connected surface over $\mathbf{F}_q$, where $\operatorname{char} \mathbf{F}_q=p>2$, and let $\ell\neq p$ be a prime. The Artin–Tate…

Let $\mathcal{E}_{2^r}$ denote the exceptional pairing on the cyclic group of order $2^r$, as used in the paper. For an integer $k\geq 1$, consider the direct product of $k$ copies…

Let $G$ be a finite graph, and let $\Gamma=\operatorname{Jac}(G)$ be its Jacobian, equipped with its canonical monodromy pairing … For a finite abelian group with pairing…

Vercauteren's lower-bound conjecture. Any non-degenerate pairing on $E$ requires at least