Recently, I read 'the red book of varieties and schemes' written by Professor Daivd Mumford. At page 65, he wrote that ' A much deeper connetion is given by class field theory, between the tower of number fields and the tower of coverings of an algebraic curve defined over a finite field.'. In this paragraph, he wanted to give an example of the analogy vetween arithmetic and geometric questions.
I know the main theorems of CFT, but I'm not familiar with the proof. Thus, I'm interesting with this result and wish it can give me a interesting proof. However, when I searched this result, I can only find 'geometric CFT', which is over function fields.
So I'm wondering if there is some reference about this result? Or the 'geometric CFT' is linked with this result?
Thanks in advance.
2026-03-29 19:44:46.1774813486
Reference request for class field theory in arithmetic geometry
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