Examples of extensions with Demushkin group

Tsvetkov, V. M.

doi:10.1007/bf01094385

Cited by 3 publications

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“…The condition -lv7sso = 0 was checked by V. M. Tsvetkov [17] in case (1), and by L. V. Kuz'min [6], V. M. Tsvetkov [17] respectively in case (2).…”

Section: Weak Leopoldt Conjecturementioning

confidence: 99%

A note on free pro-$p$-extensions of algebraic number fields

Yamagishi¹

1993

Journal De Théorie Des Nombres De Bordeaux

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L'accès aux archives de la revue « Journal de Théorie des Nombres de Bordeaux » (http://jtnb.cedram.org/) implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ 165-1 A note on free pro-p-extensions of algebraic number fields par MASAKAZU YAMAGISHIABSTRACT. For an algebraic number field k and a prime p, define the number p to be the maximal number d such that there exists a Galois extension of k whose Galois group is a free pro-p-group of rank d. The Leopoldt conjecture implies 1~ p ~ r2 +1, (r2 denotes the number of complex places of k). Some examples of k and p with 03C1 = r2 + 1 have been known so far. In this note, the invariant 03C1 is studied, and among other things some examples with p r2 + 1 are given.197-208.

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“…The condition -lv7sso = 0 was checked by V. M. Tsvetkov [17] in case (1), and by L. V. Kuz'min [6], V. M. Tsvetkov [17] respectively in case (2).…”

Section: Weak Leopoldt Conjecturementioning

confidence: 99%