Abstract
In this chapter, we give the main results of global class field theory for the case of number fields. We refer the reader to [Art-Tat], [Gras], [Has1], [Jan], or [Mart4] for more detailed statements and proofs. We present the results “à la Hasse”, without using ideles. This is more suitable for algorithmic treatment. For an idelic treatment, we refer to [Neu]. I have largely benefited from the notes of J. Martinet [Mart4] in writing this chapter.
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© 2000 Springer Science+Business Media New York
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Cohen, H. (2000). The Fundamental Theorems of Global Class Field Theory. In: Advanced Topics in Computational Number Theory. Graduate Texts in Mathematics, vol 193. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8489-0_3
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DOI: https://doi.org/10.1007/978-1-4419-8489-0_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6419-4
Online ISBN: 978-1-4419-8489-0
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