Division Algebras and Quadratic Reciprocity
Timothy J. Ford
TL;DR
This paper applies advanced algebraic tools to derive reciprocity laws for power residues, enhancing understanding of quadratic reciprocity through the lens of division algebras and Brauer groups.
Contribution
It introduces new reciprocity laws for qth power residues using Grothendieck and Artin-Mumford sequences in the context of division algebras.
Findings
Derived new reciprocity laws for qth power residues.
Connected Brauer group sequences to quadratic reciprocity.
Extended algebraic frameworks for understanding power residue symbols.
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 th power residues.
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Taxonomy
TopicsAdvanced Topics in Algebra · Polynomial and algebraic computation · Rings, Modules, and Algebras