K 2 et conjecture de Greenberg dans les p -extensions multiples
Journal de théorie des nombres de Bordeaux, Volume 17 (2005) no. 2, p. 669-688

For a number field K containing a primitive p-th root of unity, we study a sufficient condition, in terms of K 2 , for the validity of Greenberg’s generalized conjecture. This applies to cyclotomic fields (μ p ) satisfying certain conditions, e.g. (μ 37 ).

Pour un corps de nombres K contenant une racine primitive p-ième de l’unité, nous proposons une condition suffisante, en termes de K 2 , pour la validité de la conjecture de Greenberg généralisée. Celle-ci s’applique pour les corps cyclotomiques vérifiant certaines conditions, par exemple (μ 37 ).

@article{JTNB_2005__17_2_669_0,
     author = {Nguyen Quang Do, Thong and Vauclair, David},
     title = {$K\_2$ et conjecture de Greenberg dans les $\mathbb{Z}\_p$-extensions multiples},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux 1},
     volume = {17},
     number = {2},
     year = {2005},
     pages = {669-688},
     doi = {10.5802/jtnb.513},
     mrnumber = {2211313},
     zbl = {1091.11041},
     language = {fr},
     url = {http://www.numdam.org/item/JTNB_2005__17_2_669_0}
}
Nguyen Quang Do, Thong; Vauclair, David. $K_2$ et conjecture de Greenberg dans les $\mathbb{Z}_p$-extensions multiples. Journal de théorie des nombres de Bordeaux, Volume 17 (2005) no. 2, pp. 669-688. doi : 10.5802/jtnb.513. http://www.numdam.org/item/JTNB_2005__17_2_669_0/

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