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2008•Mathematical Research LettersRequires access

Chevalley’s ambiguous class number formula for an arbitrary torus

Cristian D. González-Avilés

Open publisher page 14 citations

Abstract

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 = Gm 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. 1.

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What this paper is about

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 = Gm 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. 1.

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Available abstract

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 = Gm 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. 1.

Key concepts: Mathematics, Torus, Class (philosophy), Pure mathematics, Algebra over a field, Geometry, Epistemology, Philosophy

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