### Relative K-theory and class field theory for arithmetic surfaces, by Alexander Schmidt

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
CH_0(X,Y) 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,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: CH_0(X,Y) ---> \tilde \pi_1^t(X,Y)^{ab}
Both groups are finite.

Alexander Schmidt <schmidt@mathi.uni-heidelberg.de>