Sur la capitulation des 2-classes d'idéaux du corps Q(√(2p₁p₂), i)

2015/03/17 by Abdelmalek Azizi, Azizi, Abdelmalek, Abdelkader Zekhnini +3
Mathematics · #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1503.05132

6 pages, in French in Workshop International "Théorie des Nombres, Codes, Cryptographie et Systèmes de Communication", du 26 au 28 Avril 2012 01/2012

arxiv created 2015/03/17 · openalex publication_date 2015/03/17 · arxiv updated 2015/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p₁ and p₂ be two primes such that p₁≡ p₂≡1 \pmod4 and at least two of the three elements \((2)/(p₁)), ((2)/(p₂)), ((p₁)/(p₂))\ are equal to -1. Put i=√(-1), d=2p₁p₂ and k =Q(√(d), i). Let k₂⁽¹⁾ be the Hilbert 2-class field of k and k^(*)=Q(√(p₁),√(p₂),√ 2, i) be its genus field. Let C_k,2 denote the 2-part of the class group of k. The unramified abelian extensions of k are K₁=k(√(p₁)), K₂=k(√(p₂)), K₃=k(√(2)) and k^(*). Our goal is to study the capitulation problem of the 2-classes of k in these four extensions.

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