Covering data and higher dimensional global class field theory
Number Theory
2009-03-17 v2 Algebraic Geometry
Abstract
For a connected regular scheme X, flat and of finite type over Spec(Z), we construct a reciprocity homomorphism \rho_X: C_X --> \pi_1^\ab(X), which is surjective and whose kernel is the connected component of the identity. The (topological) group C_X is explicitly given and built solely out of data attached to points and curves on X. A similar but weaker statement holds for smooth varieties over finite fields. Our results are based on earlier work of G. Wiesend.
Cite
@article{arxiv.0804.3419,
title = {Covering data and higher dimensional global class field theory},
author = {Moritz Kerz and Alexander Schmidt},
journal= {arXiv preprint arXiv:0804.3419},
year = {2009}
}
Comments
31 pages, corrected minor mistakes and added some remarks