Hilbert's tenth problem for algebraic function fields of characteristic 2

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

Let K be an algebraic function field of characteristic 2 with constant field CK. Let C be the algebraic closure of a finite field in K. Assume that C has an extension of degree 2. Assume that there are elements u, x of K with u transcendental over CK and x algebraic over C(u) and such that K = CK(u, x). Then Hilbert's Tenth Problem over K is undecidable. Together with Shlapentokh's result for odd characteristic this implies that Hilbert's Tenth Problem for any such field K of finite characteristic is undecidable. In particular, Hilbert's Tenth Problem for any algebraic function field with finite constant field is undecidable.

Original languageEnglish (US)
Pages (from-to)261-281
Number of pages21
JournalPacific Journal of Mathematics
Volume210
Issue number2
DOIs
StatePublished - Jun 2003

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Hilbert's tenth problem for algebraic function fields of characteristic 2'. Together they form a unique fingerprint.

Cite this