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Algebra |
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Authors: Lucian M Ionescu
Galois theory in the category of cyclic groups studies the automorphism groups of the cyclic group extensions and the corresponding Galois connection. The theory can be rephrased in dual terms of quotients, corresponding to extensions, when viewed as covering maps. The computation of Galois groups and stating the associated Galois connection are based on already existing work regarding the automorphism groups of finite p-adic groups. The initial goals for developing such a theory were: pedagogical, to introduce the basic language of Category Theory, while exposing the student to core ideas of Galois Theory, but also targeting applications to the Galois Theory of cyclotomic extensions. Some aspects of Abelian Class Field Theory and Anabelian Geometry are also mentioned.
Comments: 8 Pages.
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[v1] 2022-04-18 15:44:02
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