Diophantine undecidability over algebraic function fields over finite fields of constants
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Publication:1915694
DOI10.1006/jnth.1996.0080zbMath0856.11058OpenAlexW2035776188MaRDI QIDQ1915694
Publication date: 5 March 1997
Published in: Journal of Number Theory (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/jnth.1996.0080
existence of solutionsfunction field over a finite fieldexistential theoryanalogue of Hilbert's Tenth problemdiophantine undecidability
Arithmetic theory of algebraic function fields (11R58) Decidability (number-theoretic aspects) (11U05) Decidability of theories and sets of sentences (03B25) Multiplicative number theory (11N99)
Related Items (11)
Hilbert's tenth problem over function fields of positive characteristic not containing the algebraic closure of a finite field ⋮ ELLIPTIC CURVE POINTS AND DIOPHANTINE MODELS OF ℤ IN LARGE SUBRINGS OF NUMBER FIELDS ⋮ The work of Kim and Roush on questions of decidability in algebra and number theory ⋮ Uniform existential interpretation of arithmetic in rings of functions of positive characteristic ⋮ Diophantine undecidability for some function fields of infinite transcendence degree and positive characteristic ⋮ Hilbert's tenth problem for function fields of varieties over algebraically closed fields of positive characteristic ⋮ An existential divisibility lemma for global fields ⋮ Diophantine undecidability of holomorphy rings of function fields of characteristic 0 ⋮ Integrality at a prime for global fields and the perfect closure of global fields of characteristic \(p > 2\) ⋮ DIOPHANTINE DEFINABILITY OVER HOLOMORPHY RINGS OF ALGEBRAIC FUNCTION FIELDS WITH INFINITE NUMBER OF PRIMES ALLOWED AS POLES ⋮ On Dipphantine definability and decidability in some rings of algebraic functions of characteristic 0
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