Moritz Kerz and Alexander Schmidt: Covering data and higher dimensional class field theory

       Authors: Moritz Kerz and Alexander Schmidt
       Title: Covering data and higher dimensional class field theory
       Pages: 31
       in: J. of Number Theory 129 (2009), 2569-2599

Preprint pdf-file covdat-kkt.pdf Corrections: covdat-cor.pdf

	Abstract: For a connected regular scheme X, flat and of finite type over Spec(Z), we construct a reciprocity homomorphism &rho_X: C_X --> &pi₁^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.

Abstract: For a connected regular scheme X, flat and of finite type over Spec(Z), we construct a reciprocity homomorphism &rho_X: C_X --> &pi₁^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.

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