Chevalley's ambiguous class number formula for an arbitrary torus

Details Chevalley's ambiguous class number formula for an arbitrary torus Chevalley's ambiguous class number formula for an arbitrary torus

2007-11-10

arxiv.org/abs/0711.1623v2

Mathematics

Number Theory

19 pages

Scientific paper

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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