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On the Tamagawa Number of Algebraic Tori

1963/07/01 by Takashi Ono · 106 citations
Mathematics · #Advanced Topics in Algebra #Finite Group Theory Research #Algebraic Geometry and Number Theory #Mathematics #Torus #Algebraic number #Pure mathematics #Geometry #Mathematical analysis

paper · doi:10.2307/1970502

published in Annals of Mathematics 78(1), 47 (Princeton University)

openalex publication_date 1963/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2025/11/06

Abstract

Introduction 1. Extensions and cross sections 1.1. Extensions 1.2. Cross sections 2. Nakayama's duality 2.1. Preliminaries 2.2. Nakayama's duality 2.3. Some sequences 3. The numbers T(T), h(T) and i(T) 3.1. Functorial properties 3.2. The number r(T) 3.3. The number h(T) 3.4. The number i(T) 4. The numbers T(E), h(E) and i(E) 4.1. A function f (E) 4.2. The number T(E) 4.3. Proof of (Al), (A2) 4.4. Relation among r(E), h(E) and i(E) 4.5. Cyclic splitting field 5. Main theorem 6. Examples 6.1. The sequence (N) 6.2. Construction of T with T(T) E Z 6.3. An example of semi-simple group G with z(G) E Z References

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