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Sur la séparation des caractères par les Frobenius
Euvrard, Charlotte (Université Bourgogne France-Comté. Laboratoire de Mathématiques de Besançon)
Maire, Christian (Université Bourgogne France-Comté. Laboratoire de Mathématiques de Besançon)

Data: 2017
Resum: In this paper, we are interested in the question of separating two characters of the absolute Galois group of a number field K, by the Frobenius of a prime ideal p of OK. We first recall an upper bound for the norm N(p) of the smallest such prime p, depending on the conductors and on the degrees. Then we give two applications: (i) find a prime number p for which P (mod p) has a certain type of factorization in Fp[X], where P ∈ Z[X] is a monic, irreducible polynomial of squarefree discriminant; (ii) on the estimation of the maximal number of tamely ramified extensions of Galois group An over a fixed number field K. To finish, we discuss some statistics in the quadratic number fields case (real and imaginary) concerning the separation of two irreducible unramified characters of the alterning group An,for n = 5, 7, 13.
Drets: Tots els drets reservats
Llengua: Anglès.
Document: article ; recerca ; publishedVersion
Matèria: Chebotarev density theorem ; Frobenius ; Unramified extensions ; Irreducible characters
Publicat a: Publicacions matemàtiques, Vol. 61 Núm. 2 (2017) , p. 475-515 (Articles) , ISSN 2014-4350

Adreça original: https://www.raco.cat/index.php/PublicacionsMatematiques/article/view/327588
DOI: 10.5565/PUBLMAT6121706

41 p, 2.4 MB

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