Diophantine subsets of function fields of curves

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We consider diophantine subsets of function fields of curves and show, roughly speaking, that they are either very small or very large. In particular, this implies that the ring of polynomials k[t] is not a diophantine subset of the field of rational functions k(t) for many fields k.

Original languageEnglish (US)
Pages (from-to)299-311
Number of pages13
JournalAlgebra and Number Theory
Issue number3
StatePublished - 2008

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


  • Diophantine set
  • Rationally connected variety


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