Covering data and higher dimensional global class field theory

2008/04/22 by Moritz Kerz, Alexander Schmidt, Kerz, Moritz +1
Mathematics · #11R37 #19F05 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0804.3419

openalex publication_date 2008/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a connected regular scheme X, flat and of finite type over Spec(Z), we construct a reciprocity homomorphism ρ_X: C_X --> π₁^\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.

Citations

• Higher class field theory and the connected component

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