Higher reciprocity law and an analogue of the Grunwald-Wang theorem for the ring of polynomials over an ultra-finite field

DOI10.1016/j.apal.2024.103438arXiv2309.02734OpenAlexW4392907590MaRDI QIDQ6131203

Ngoc Dong Quan Nguyen

Publication date: 4 April 2024

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

Full work available at URL: https://arxiv.org/abs/2309.02734

zbMATH Keywords

ultraproductGrunwald-Wang theoremhigher reciprocity law

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Polynomials in general fields (irreducibility, etc.) (12E05) Class field theory (11R37) Ultraproducts and related constructions (03C20)

Cites Work

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• The use of ultraproducts in commutative algebra
• Model theory of finite fields and pseudo-finite fields
• Model theory
• The Riemann hypothesis in characteristic \(p\) in historical perspective
• Reciprocity by resultant in \(k[t\)]
• The elementary theory of finite fields
• Field Arithmetic
• The Arithmetic of Polynomials in a Galois Field
• Valued Fields