Resumen de Chevalley's ambiguous class number formula for an arbitrary torus

Cristian D. González Avilés

• 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 N\'eron-Raynaud models of tori.