$R$-equivalence on Cubic Surfaces I: Existing Cases with Non-Trivial Universal Equivalence

Dimitri Kanevsky, Julian Salazar, Matt Harvey

Let $V$ be a smooth cubic surface over a $p$-adic field $k$ with good reduction. Swinnerton-Dyer (1981) proved that $R$-equivalence is trivial on $V(k)$ except perhaps if $V$ is on…