Abstract
Let X be a regular arithmetic scheme, i.e. a regular integral separated scheme flat and of finite type over Spec \({\mathbb{Z}}\) . Generalising classical class field theory for number fields, we define a class group CX and show there is a natural surjective map \({C_X\rightarrow\pi_1^{ab}(X)}\) whose kernel is the connected component of 0.
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