Undecidability in function fields of positive characteristic

Anne Kirsten Eisentraeger, Alexandra Shlapentokh

Research output: Contribution to journalArticle

6 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)4051-4086
Number of pages36
JournalInternational Mathematics Research Notices
Volume2009
Issue number21
DOIs
StatePublished - Dec 1 2009

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Undecidability
Positive Characteristic
Function Fields
Elliptic Curves
Galois field
First-order
Ring

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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Undecidability in function fields of positive characteristic. / Eisentraeger, Anne Kirsten; Shlapentokh, Alexandra.

In: International Mathematics Research Notices, Vol. 2009, No. 21, 01.12.2009, p. 4051-4086.

Research output: Contribution to journalArticle

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