Relative K-theory and class field theory for arithmetic surfaces
Number Theory
2007-05-23 v1 Algebraic Geometry
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 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.
Cite
@article{arxiv.math/0204330,
title = {Relative K-theory and class field theory for arithmetic surfaces},
author = {Alexander Schmidt},
journal= {arXiv preprint arXiv:math/0204330},
year = {2007}
}
Comments
32 pages