Factorial Fermat curves over the rational numbers
Volume 142 / 2016
Colloquium Mathematicum 142 (2016), 285-300
MSC: Primary 13F15; Secondary 14H05.
DOI: 10.4064/cm142-2-9
Abstract
A polynomial $f$ in the set $\{X^{n}+Y^{n}, X^{n} +Y^{n}-Z^{n}, X^{n} +Y^{n}+Z^{n}, X^{n} +Y^{n}-1\}$ lends itself to an elementary proof of the following theorem: if the coordinate ring over $\mathbb {Q}$ of $f$ is factorial, then $n$ is one or two. We give a list of problems suggested by this result.
