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Algebraic Number Theory and the Kronecker-Weber Theorem1131 views
Author
Baugher, Zachary, Mathematics, University of Virginia
Advisors
Rapinchuk, Andrei, AS-Mathematics, University of Virginia
Abstract
The goal of this work is to prove the Kronecker-Weber theorem, an important first step to classifying abelian extensions of number fields. In chapter 1, we review the crucial concepts of Dedekind rings and ramification. Chapter 2 proceeds to study cyclotomic fields, ultimately developing the tools of ramification groups and the different. In chapter 3 we prove the main theorem, including two different proofs for the key statement to which we reduce the theorem for odd primes. We conclude with a brief look at the next steps, namely class field theory and Kronecker's Jugendtraum.
Degree
BA (Bachelor of Arts)
Keywords
Hilbert's twelfth problem; cyclotomic fields; Jugendtraum; algebraic number theory
Baugher, Zachary. Algebraic Number Theory and the Kronecker-Weber Theorem. University of Virginia, Mathematics, BA (Bachelor of Arts), 2021-05-07, https://doi.org/10.18130/pvkq-cp94.