Elliptic curves and Hilbert’s tenth problem for algebraic function fields over real andp-adic fields

DOI10.1515/crll.2005.2005.587.77zbMath1085.14029arXivmath/0409103OpenAlexW2049996134MaRDI QIDQ5701252

Laurent Moret-Bailly

Publication date: 2 November 2005

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0409103

zbMATH Keywords

elliptic curves\(p\)-adic fieldsHilbert's tenth problemreal fields

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Decidability (number-theoretic aspects) (11U05) Decidability and field theory (12L05) Elliptic curves over global fields (11G05) Decidability of theories and sets of sentences (03B25) Other nonalgebraically closed ground fields in algebraic geometry (14G27)

Related Items (12)

Uniform first-order definitions in finitely generated fields ⋮ The work of Kim and Roush on questions of decidability in algebra and number theory ⋮ Hilbert's Tenth problem for function fields of varieties over number fields and \(p\)-adic fields ⋮ On existential definitions of c.e. subsets of rings of functions of characteristic 0 ⋮ Some aspects of rational points and rational curves ⋮ Algebraic cycles from a computational point of view ⋮ Hilbert's tenth problem for function fields of varieties over algebraically closed fields of positive characteristic ⋮ Diophantine sets of polynomials over number fields ⋮ Julia Robinson numbers ⋮ 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 ⋮ Definability and decidability in infinite algebraic extensions

Cites Work

• Abeliants and their application to an elementary construction of Jacobians.
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