>>250 追加

類体論の一般化には、下記３つあって
1つは、the Langlands correspondence
1つは、anabelian geometry
1つは、higher class field theory

anabelian geometry が出てくるのが面白。IUTに関連

Langlands programは、
”・・to non-abelian extensions. This generalization is mostly still conjectural. For number fields, class field theory and the results related to the modularity theorem are the only cases known.”
とあるね。the modularity theorem＝谷山?志村予想だね

https://en.wikipedia.org/wiki/Modularity_theorem
Modularity theorem
https://ja.wikipedia.org/wiki/%E8%B0%B7%E5%B1%B1%E2%80%93%E5%BF%97%E6%9D%91%E4%BA%88%E6%83%B3
谷山?志村予想

https://en.wikipedia.org/wiki/Class_field_theory#Generalizations_of_class_field_theory
Class field theory
(抜粋)
In mathematics, class field theory is the branch of algebraic number theory concerned with the abelian extensions of number fields, global fields of positive characteristic, and local fields.
The theory had its origins in the proof of quadratic reciprocity by Gauss at the end of 18th century. These ideas were developed over the next century, giving rise to a set of conjectures by Hilbert that were subsequently proved by Takagi and Artin.
These conjectures and their proofs constitute the main body of class field theory.

つづく