July 3, 2024Open Access

Division Algebras and Quadratic Reciprocity

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Abstract

The Grothendieck and Artin-Mumford exact sequences for the Brauer group of a function field in 1 or 2 variables are applied to derive reciprocity laws for qth power residues.

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Timothy J. Ford (Wed,) studied this question.

synapsesocial.com/papers/68e6191db6db6435875abf7f https://doi.org/https://doi.org/10.48550/arxiv.2407.03447

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3On special triples of algebras over the rational function field2026
4Canonical Sections of Artin–Schreier–Witt Extensions and an Algebraic Expression of the Reciprocity Map in Local Fields of Characteristic p2026
5(Algebraic) $ p $-adic Artin formalism of twisted triple product Galois representations over real quadratic fields2025

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