Tame class field theory for arithmetic schemes

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. Theorem: There exists a natural reciprocity isomorphism \[ \rec_{X,D}: \CH_0(X,D) \liso \tilde \pi_1^t(X,D)^\ab\. \] Both groups are finite. This paper corrects and generalizes my paper "Relative K-theory and class field theory for arithmetic surfaces" (math.NT/0204330)