Rational points on even‐dimensional Fermat cubics

We show that even‐dimensional Fermat cubic hypersurfaces are rational over any field of characteristic not equal to three, by constructing explicit rational parameterizations with polynomials of low degree. As a byproduct of our rationality constructions, we obtain estimates for the number of their rational points over a number field and exhibit a class of quadro‐cubic Cremona correspondences in even‐dimensional projective spaces.