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Factorial Fermat curves over the rational numbers

Tom 142 / 2016

Peter Malcolmson, Frank Okoh, Vasuvedan Srinivas Colloquium Mathematicum 142 (2016), 285-300 MSC: Primary 13F15; Secondary 14H05. DOI: 10.4064/cm142-2-9

Streszczenie

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.

Autorzy

  • Peter MalcolmsonDepartment of Mathematics
    Wayne State University
    Detroit, MI 48202, U.S.A.
    e-mail
  • Frank OkohDepartment of Mathematics
    Wayne State University
    Detroit, MI 48202, U.S.A.
    e-mail
  • Vasuvedan SrinivasSchool of Mathematics
    Tata Institute of Fundamental Research
    Mumbai 400005, India
    e-mail

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