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Abstract: We extend the unramified class field theory for arithmetic schemes of K. Kato and S. Saito to the tame case. Let X be a regular proper arithmetic scheme and let D be a divisor on X whose vertical irreducible components are normal schemes. Let CH_0(X,D) denote the relative Chow group of zero cycles and let \tilde \pi_1^t(X,Y)^ {ab} denote the abelianized modified tame fundamental group of (X,D) (which classifies finite etale abelian coverings of X-supp(D) which are tamely ramified along D and in which every real point splits completely).
THEOREM: There exists a natural reciprocity isomorphism rec: CH_0(X,D) ---> \tilde \pi_1^t(X,D)^ {ab} . Both groups are finite |