Undecidability in function fields of positive characteristic

Details Undecidability in function fields of positive characteristic Undecidability in function fields of positive characteristic

2007-09-12

arxiv.org/abs/0709.1739v2

Mathematics

Number Theory

12 pages; strengthened main theorem, proved undecidability in the language of rings without parameters

Scientific paper

We prove that the first-order theory of any function field K of characteristic p>2 is undecidable in the language of rings without parameters. When K is a function field in one variable whose constant field is algebraic over a finite field, we can also prove undecidability in characteristic 2. The proof uses a result by Moret-Bailly about ranks of elliptic curves over function fields.

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