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arXiv · 0804.3419

Covering data and higher dimensional global class field theory

Moritz Kerz·Alexander Schmidt
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Abstract

For a connected regular scheme X, flat and of finite type over Spec(Z), we construct a reciprocity homomorphism ρ_X: C_X --> π_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.

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Moritz Kerz, Alexander Schmidt. 2009-03-17. Covering data and higher dimensional global class field theory. https://arxiv.org/abs/0804.3419

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