Discoveries / algebra

Manin's Question on R-Equivalence for the Diagonal Cubic

Swinnerton-Dyer (1981) proved $R$-equivalence trivial on smooth cubic surfaces over $p$-adic fields with good reduction, except for three special types. The paper resolves two long-standing exceptional cases: triviality for the diagonal cubic over $\mathbb{Q}_3$, answering a question from Manin's Cubic Forms (1972), and the cubic with universal equivalence of exponent 2 (Kanevsky, 1982).