Class field theory for open curves over local fields

Abstract

Theory for open curves over a local field. After introducing the reciprocity map, we determine the kernel and the cokernel of this map. In addition to this, the Pontrjagin dual of the reciprocity map is also investigated. This gives the one to one correspondence between the set of finite abelian \'etale coverings and the set of finite index open subgroups of the id\`ele class group as in the classical class field theory under some assumptions.