A Quick Tour of Class Field Theory
One could argue that the principal goal of number theory is to understand the integral or rational solutions of systems of Diophantine equations; that is, polynomial equations with integral coefficients. Nineteenth-century mathematicians, mainly riding the impetus provided by attempts to tackle the Fermat equation x n +y n =z n (n≥3), realized the benefits of studying the solutions in extended number systems R, as opposed to confining one’s attention to only Z and Q, and this led eventually to global and local fields and their rings of integers.
KeywordsConjugacy Class Galois Group Open Subgroup Residue Field Global Field
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