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March 21, 2026Transactions of the London Mathematical Society0 citationsOpen Access

Rational points on even‐dimensional Fermat cubics

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AMAlex Massarenti

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.

Abstract

Abstract 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.

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Cite This Study

Alex Massarenti (2026) studied this question.

synapsesocial.com/papers/69be35d76e48c4981c67458bhttps://doi.org/10.1112/tlm3.70028
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