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Algebra |
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Authors: Lucian M Ionescu
The main goal of Class Field Theory, of characterizing abelian field extensions in terms of the arithmetic of the rationals, is achieved via the correspondence between Arithmetic Galois Theory and classical (algebraic) Galois Theory, as formulated in its traditional form by Artin. The analysis of field extensions, primarily of the way rational primes decompose in field extensions, is proposed, in terms of an invariant of the Galois group encoding its structure. Prospects of the non-abelian case are given in terms of Grothendieck's Anabelian Theory.
Comments: 4 Pages.
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[v1] 2022-05-05 11:39:02
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