Diophantine unsolvability over \(p\)-adic function fields

DOI10.1006/jabr.1995.1234zbMath0858.12006OpenAlexW1986243492MaRDI QIDQ1899086

Fred W. Roush, Kim Hang Kim

Publication date: 9 November 1995

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.1995.1234

zbMATH Keywords

rational function fieldnonarchimedean local fieldalgorithmic unsolvability of diophantine equationsdecision methods for isotropy

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Decidability (number-theoretic aspects) (11U05) Decidability and field theory (12L05) Decidability of theories and sets of sentences (03B25) Non-Archimedean valued fields (12J25)

Related Items (20)

Uniform first-order definitions in finitely generated fields ⋮ DIOPHANTINE SETS OF POLYNOMIALS OVER ALGEBRAIC EXTENSIONS OF THE RATIONALS ⋮ The work of Kim and Roush on questions of decidability in algebra and number theory ⋮ The publications of Ki Hang Kim ⋮ Hilbert's Tenth problem for function fields of varieties over number fields and \(p\)-adic fields ⋮ Diophantine undecidability for some holomorphy rings of algebraic functions of characteristic 0. ⋮ The logic of pseudo-\(S\)-integers ⋮ On existential definitions of c.e. subsets of rings of functions of characteristic 0 ⋮ Hilbert's tenth problem for rational function fields over \(p\)-adic fields ⋮ Some aspects of rational points and rational curves ⋮ Hilbert's tenth problem for rings of rational functions ⋮ Diophantine undecidability for some function fields of infinite transcendence degree and positive characteristic ⋮ Grothendieck Rings of ℤ-Valued Fields ⋮ Hilbert's tenth problem for function fields of varieties over algebraically closed fields of positive characteristic ⋮ Diophantine sets of polynomials over number fields ⋮ Powerful values of polynomials and a conjecture of Vojta ⋮ Diophantine undecidability of holomorphy rings of function fields of characteristic 0 ⋮ First-order definitions of rational functions and \({\mathcal S}\)-integers over holomorphy rings of algebraic functions of characteristic 0 ⋮ 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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