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Mathematics > Number Theory

arXiv:0709.1739 (math)
[Submitted on 12 Sep 2007 (v1), last revised 27 Feb 2008 (this version, v2)]

Title:Undecidability in function fields of positive characteristic

Authors:Kirsten Eisentraeger, Alexandra Shlapentokh
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Abstract: 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.
Comments: 12 pages; strengthened main theorem, proved undecidability in the language of rings without parameters
Subjects: Number Theory (math.NT); Logic (math.LO)
MSC classes: 11U05 (Primary); 03B25 (Secondary)
Cite as: arXiv:0709.1739 [math.NT]
  (or arXiv:0709.1739v2 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.0709.1739

Submission history

From: Kirsten Eisentraeger [view email]
[v1] Wed, 12 Sep 2007 01:29:37 UTC (15 KB)
[v2] Wed, 27 Feb 2008 02:16:12 UTC (15 KB)
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