Integrality at a prime for global fields and the perfect closure of global fields of characteristic \(p > 2\)

DOI10.1016/j.jnt.2005.02.008zbMath1137.11358arXivmath/0310224OpenAlexW2101217013MaRDI QIDQ2566189

Kirsten Eisenträger

Publication date: 22 September 2005

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0310224

zbMATH Keywords

Brauer groupHilbert's Tenth ProblemUndecidabilityDiophantine definition

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Decidability (number-theoretic aspects) (11U05) Undecidability and degrees of sets of sentences (03D35) Decidability of theories and sets of sentences (03B25)

Related Items (2)

Irreducibility of polynomials over global fields is diophantine ⋮ Diophantine definability of nonnorms of cyclic extensions of global fields

Cites Work

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• Hilbert's tenth problem for fields of rational functions over finite fields
• The decision problem for exponential diophantine equations
• Diophantine undecidability of \({\mathbb{C}{}}(t_ 1,t_ 2)\)
• Diophantine classes of holomorphy rings of global fields
• Hilbert's tenth problem for algebraic function fields over infinite fields of constants of positive characteristic
• Diophantine undecidability over algebraic function fields over finite fields of constants
• The Undecidability of Algebraic Rings and Fields
• Undecidability and Definability for the Theory of Global Fields
• The Diophantine Problem for Polynomial Rings and Fields of Rational Functions
• Hilbert's Tenth Problem for Rational Function Fields in Characteristic 2
• Definability and decision problems in arithmetic

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