Rational points on even‐dimensional Fermat cubics

Key Points

• The aim is to demonstrate that even-dimensional Fermat cubic hypersurfaces are rational over fields with characteristic not equal to three.
• Construct explicit rational parameterizations using low degree polynomials.
• Estimate the number of rational points over number fields.
• Exhibit a class of quadro-cubic Cremona correspondences in projective spaces.
• Even-dimensional Fermat cubics are shown to be rational over applicable fields.
• Rational parameterizations were successfully constructed.
• Insights into the distribution of rational points were obtained.