Universally defining finitely generated subrings of global fields

DOI10.25537/dm.2021v26.1851-1869zbMath1486.11156arXiv1812.04372OpenAlexW4313680829MaRDI QIDQ2062179

Nicolas Daans

Publication date: 27 December 2021

Published in: Documenta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.04372

zbMATH Keywords

definabilityglobal fieldsquaternion algebradiophantine definabilityDiophantine setHilbert 10th problem

Mathematics Subject Classification ID

Quaternion and other division algebras: arithmetic, zeta functions (11R52) Interpolation, preservation, definability (03C40) Model theory (number-theoretic aspects) (11U09)

Related Items

Universally defining Z$\mathbb {Z}$ in Q$\mathbb {Q}$ with 10 quantifiers

Cites Work

• Universally and existentially definable subsets of global fields
• Introduction to quadratic forms
• A universal first-order formula defining the ring of integers in a number field
• Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas. (Séconde partie)
• Solution of the congruence subgroup problem for \(\text{SL}_ n\) \((n\geq 3)\) and \(\text{Sp}_{2n}\) \((n\geq 2)\)
• Characterizing integers among rational numbers with a universal-existential formula
• Irreducibility of polynomials over global fields is diophantine
• Valued Fields
• Definability and decision problems in arithmetic
• Defining \(\mathbb Z\) in \(\mathbb Q\)
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