An example of a non-associative Moufang loop of point classes on a cubic surface

Dimitri Kanevsky

Let $V$ be a cubic surface defined by the equation $T_0^3+T_1^3+T_2^3+\theta T_3^3=0$ over a quadratic extension of 3-adic numbers $k={\mathbb{Q}}_3(\theta )$, where ${\theta }^3=1$. We show that a rela…