Chevalley's ambiguous class number formula for an arbitrary torus

2007/11/10 by Cristian D. González-Avilés, Gonzalez-Aviles, Cristian D.
Mathematics · #11R99 #20G30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0711.1623

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

Abstract

This version is a significant improvement of the original paper. It includes a new section where we discuss norm tori in some detail. The new abstract is the following: In this paper we obtain Chevalley's ambiguous class number formula for an arbitrary torus T over a global field. The classical formula of C.Chevalley may be recovered by setting T=G_m in our formula. As an illustration of the general result, we discuss norm tori in detail. A key ingredient of the proof of our main theorem is the work of X.Xarles on groups of components of Neron-Raynaud models of tori.

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