Relative K-theory and class field theory for arithmetic surfaces
Alexander Schmidt
Abstract
In this paper we extend the unramified class field theory for arithmetic surfaces of K. Kato and S. Saito to the relative case. Let X be a regular proper arithmetic surface and let Y be the support of divisor on X. Let CH0(X,Y) denote the relative Chow group of zero cycles and let π1t(X,Y) ab denote the abelianized modified tame fundamental group of (X,Y) (which classifies finite etale abelian covings of X-Y which are tamely ramified along Y and in which every real point splits completely). THEOREM: There exists a natural reciprocity isomorphism rec: CH0(X,Y) --> π1t(X,Y)ab. Both groups are finite.
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