It is used in homotopy theory (topological modular/automorphic forms). Class field theory is used e.g. in this article http://front.math.ucdavis.edu/math.AT/0607665 of Niko Naumann.

Also, it is a trend in algebraic geometry to reduce geometric questions to finitely generated fields, so to the realm of arithmetic geometry.

It is used in homotopy theory (topological modular/automorphic forms). Class field theory is used e.g. in this article

• Niko Naumann, Arithmetically defined dense subgroups of Morava stabilizer groups, Compositio Mathematica, 144(1) (2008) 247-270, doi:10.1112/S0010437X07003181, arXiv:math/0607665

Also, it is a trend in algebraic geometry to reduce geometric questions to finitely generated fields, so to the realm of arithmetic geometry.

It is used in homotopy theory (topological modular/automorphic forms). Class field theory is used e.g. in this article http://front.math.ucdavis.edu/math.AT/0607665

Also, it is a trend in algebraic geometry to reduce geometric questions to finitely generated fields, so to the realm of arithmetic geometry.

It is used in homotopy theory (topological modular/automorphic forms). Class field theory is used e.g. in this article http://front.math.ucdavis.edu/math.AT/0607665 of Niko Naumann.

Also, it is a trend in algebraic geometry to reduce geometric questions to finitely generated fields, so to the realm of arithmetic geometry.