Hilbert's Tenth problem for function fields of varieties over number fields and \(p\)-adic fields

DOI10.1016/j.jalgebra.2006.09.032zbMath1152.11050arXivmath/0610132OpenAlexW2129200961MaRDI QIDQ875926

Kirsten Eisenträger

Publication date: 16 April 2007

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

Full work available at URL: https://arxiv.org/abs/math/0610132

zbMATH Keywords

Rational pointsQuadratic formsElliptic curvesUndecidabilityDiophantine modelHilbert's tenth Problem

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Decidability (number-theoretic aspects) (11U05) Rational points (14G05) Basic properties of first-order languages and structures (03C07)

Related Items

Cryptanalysis of a public key cryptosystem based on Diophantine equations via weighted LLL reduction, The work of Kim and Roush on questions of decidability in algebra and number theory, On existential definitions of c.e. subsets of rings of functions of characteristic 0, Some aspects of rational points and rational curves, Hilbert's tenth problem for function fields of varieties over algebraically closed fields of positive characteristic, Diophantine sets of polynomials over number fields, Diophantine undecidability of holomorphy rings of function fields of characteristic 0, Definability and decidability in infinite algebraic extensions

Uses Software

• ecdata

Cites Work

• Hilbert's tenth problem for fields of rational functions over finite fields
• The decision problem for exponential diophantine equations
• Diophantine undecidability of \({\mathbb{C}{}}(t_ 1,t_ 2)\)
• Hilbert's tenth problem for algebraic function fields over infinite fields of constants of positive characteristic
• Hilbert's tenth problem for algebraic function fields of characteristic 2.
• Diophantine unsolvability over \(p\)-adic function fields
• Lectures on the theory of algebraic functions of one variable
• The Diophantine Problem for Polynomial Rings and Fields of Rational Functions
• Hilbert's Tenth Problem for Rational Function Fields in Characteristic 2
• Extensions of Hilbert's tenth problem
• Heights and the specialization map for families of abelian varieties.
• Elliptic curves and Hilbert’s tenth problem for algebraic function fields over real andp-adic fields
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item