Let U be a regular arithmetic surface. Assume that for all irreducible curves C subset of U there are given open normal subgroups of pi(1)(C), which fulfill a compatibility condition at all closed points x is an element of U. We then show that these data uniquely determine a normal subgroup of pi(1)(U). This is used to construct abelian class field theory for arithmetic surfaces using only K-0 and K-1 groups of local and global fields.
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