Indices isotypiques des éléments cyclotomiques

2009/12/04 by Tatiana Beliaeva, Beliaeva, Tatiana, Jean-Robert Belliard +1
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Coding theory and cryptography #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0912.0819

openalex publication_date 2009/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given F a real abelian field, p an odd prime and χ any Dirichlet character of F we give a method for computing the χ-index (H¹(G_S,ℤ_p(r))^χ: C^F(r)^χ) where the Tate twist r is an odd integer r≥ 3, the group C^F(r) is the group of higher circular units, G_S is the Galois group over F of the maximal S ramified algebraic extension of F, and S is the set of places of F dividing p. This χ-index can now be computed in terms only of elementary arithmetic of finite fields \FM_ℓ. Our work generalizes previous results by Kurihara who used the assumption that the order of χ divides p-1.

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