Higher class field theory and the connected component

Details Higher class field theory and the connected component Higher class field theory and the connected component

2007-11-28

arxiv.org/abs/0711.4485v3

Mathematics

Algebraic Geometry

Extended version includes higher class field theory

Scientific paper

In this note we present a new self-contained approach to the class field theory of arithmetic schemes in the sense of Wiesend. Along the way we prove new results on space filling curves on arithmetic schemes and on the class field theory of local rings. We show how one can deduce the more classical version of higher global class field theory due to Kato and Saito from Wiesend's version. One of our new results says that the connected component of the identity element in Wiesend's class group is divisible if some obstruction is absent.

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