Mathematical Research Letters

Volume 15 (2008)

Number 6

Chevalley’s ambiguous class number formula for an arbitrary torus

Pages: 1149 – 1165

DOI: http://dx.doi.org/10.4310/MRL.2008.v15.n6.a7

Author

Cristian D. González-Avilés (Universidad de La Serena)

Abstract

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 $T=\bg_{m}$ in our formula. A key ingredient of the proof is the work of X.Xarles on groups of components of Néron-Raynaud models of tori.

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