I know the p-adic method is important in algebraic number theory. However, in the old days, the global class field theory was developed using only ideals and classical analysis. I'm curious to know about it. Another reason is that I think the ideal theoretic approach is more constructible than the p-adic one. Since those old books and papers were written in German and I'm not at all good at German, I prefer a book written in English. Is there such a book?
Global class field theory without p-adic method
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algebraic-number-theory
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0@MakotoKato, I removed comments that were no longer relevant. – 2012-05-22
1 Answers
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You could look at Lemmermeyer's book. (It doesn't include a proof of Artin's reciprocity law, but includes proofs of the first and second inequality, and has a lot historical backgroud.)
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0@Matt Thanks! I'll check it. – 2012-04-24