Model theory of adeles. I.

DOI10.1016/j.apal.2021.103074OpenAlexW4200249780MaRDI QIDQ2067515

Jamshid Derakhshan, Angus J. Macintyre

Publication date: 18 January 2022

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.09698

zbMATH Keywords

adeles and Henselian valued fieldsHilbert symbol and reciprocityimaginaries and adele classesintegration and measure for definable setsquantifier elimination and decidabilityrestricted products and Feferman-Vaught theorems

Mathematics Subject Classification ID

Decidability (number-theoretic aspects) (11U05) Model-theoretic algebra (03C60) Zeta functions and (L)-functions of number fields (11R42) Adèle rings and groups (11R56) Model theory (number-theoretic aspects) (11U09) Quantifier elimination, model completeness, and related topics (03C10)

Related Items (4)

Between the Rings $${\mathbb Z}/p^n{\mathbb Z}$$ and the Ring $${\mathbb Z}_p$$: Issues of Axiomatizability, Definability and Decidability ⋮ Decidability of the class of all the rings : A problem of Ax ⋮ Defining \(R\) and \(G(R)\) ⋮ An undecidability result for the asymptotic theory of \(p\)-adic fields

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Some supplements to Feferman-Vaught related to the model theory of adeles
• The arithmetic site
• Uniformly defining valuation rings in Henselian valued fields with finite or pseudo-finite residue fields
• Relative elimination of quantifiers for Henselian valued fields
• Truncations of ordered abelian groups
• A class of hyperrings and hyperfields
• Formally \(p\)-adic fields
• Substructures and uniform elimination for p-adic fields
• Adèles and algebraic groups. (Appendix 1: The case of the group \(G_2\), by M. Demazure. Appendix 2: A short survey of subsequent research on Tamagawa numbers, by T. Ono)
• Model theoretic algebra. Selected topics
• Solving diophantine problems over all residue class fields of a number field and all finite fields
• Trace formula in noncommutative geometry and the zeros of the Riemann zeta function
• Quantifier elimination for Henselian fields relative to additive and multiplicative congruences
• Definable Boolean combinations of open sets are Boolean combinations of open definable sets
• Basic number theory.
• Definable equivalence relations and zeta functions of groups. With an appendix by Raf Cluckers
• The elementary theory of finite fields
• Geometry of the arithmetic site
• Schemes over 𝔽₁and zeta functions
• The first order properties of products of algebraic systems
• p-adic semi-algebraic sets and cell decomposition.
• Cell Decomposition and Local Zeta Functions in a Tower of Unramified Extensions of a p -Adic Field
• Uniform p-adic cell decomposition and local zeta functions.
• On definable subsets of p-adic fields
• Sets Definable Over Finite Fields: Their Zeta-Functions
• A.D. Alexandrov spaces with curvature bounded below
• DECIDABILITY IN LOCAL AND GLOBAL FIELDS
• Enrichments of Boolean algebras by Presburger predicates
• Diophantine Problems Over Local Fields I
• Decision procedures for real and p‐adic fields
• The hyperring of adèle classes
• Defining \(\mathbb Z\) in \(\mathbb Q\)

This page was built for publication: Model theory of adeles. I.