Higher class field theory and the connected component

2007/11/28 by Moritz Kerz, Kerz, Moritz · 1 citation
Mathematics · #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 · doi:10.48550/arxiv.0711.4485

openalex publication_date 2007/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we present a new self-contained approach to the class field theory of arithmetic schemes in the sense of Wiesend. Along the way we prove new results on space filling curves on arithmetic schemes and on the class field theory of local rings. We show how one can deduce the more classical version of higher global class field theory due to Kato and Saito from Wiesend's version. One of our new results says that the connected component of the identity element in Wiesend's class group is divisible if some obstruction is absent.

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• Covering data and higher dimensional global class field theory

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