Vanishing of degree $3$ unramified cohomology over finite fields

Federico Scavia, Fumiaki Suzuki

Let $k$ be a finite field of characteristic $p\ne 3$, let $E/k$ be the Fermat cubic curve, and let $\ell \ne p$ be a prime. If $p\equiv 1(\mathrm{mod}3)$, assume moreover that $\ell >3$. The…