A note on free pro-<span class="mathjax-formula">$p$</span>-extensions of algebraic number fields

Yamagishi, Masakazu

A note on free pro-

p

-extensions of algebraic number fields

Yamagishi, Masakazu

Journal de Théorie des Nombres de Bordeaux, Tome 5 (1993) no. 1, pp. 165-178.

Résumé

For an algebraic number field $k$ and a prime $p$ , define the number $ρ$ 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 $1 \leq ρ \leq r_{2} + 1$ , ( $r_{2}$ denotes the number of complex places of $k$ ). Some examples of $k$ and $p$ with $ρ = r_{2} + 1$ have been known so far. In this note, the invariant $ρ$ is studied, and among other things some examples with $ρ < r_{2} + 1$ are given.

MR 1251235 | Zbl 0784.11052 | 1 citation dans Numdam

Mots clés : algebraic number field,

ℤ_{p}

-extension, free pro-

p

-group

BibTeX
RIS

@article{JTNB_1993__5_1_165_0,
     author = {Yamagishi, Masakazu},
     title = {A note on free pro-$p$-extensions of algebraic number fields},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {165--178},
     publisher = {Universit\'e Bordeaux I},
     volume = {5},
     number = {1},
     year = {1993},
     zbl = {0784.11052},
     mrnumber = {1251235},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_1993__5_1_165_0/}
}

TY  - JOUR
AU  - Yamagishi, Masakazu
TI  - A note on free pro-$p$-extensions of algebraic number fields
JO  - Journal de Théorie des Nombres de Bordeaux
PY  - 1993
DA  - 1993///
SP  - 165
EP  - 178
VL  - 5
IS  - 1
PB  - Université Bordeaux I
UR  - http://www.numdam.org/item/JTNB_1993__5_1_165_0/
UR  - https://zbmath.org/?q=an%3A0784.11052
UR  - https://www.ams.org/mathscinet-getitem?mr=1251235
LA  - en
ID  - JTNB_1993__5_1_165_0
ER  -

Yamagishi, Masakazu. A note on free pro-$p$-extensions of algebraic number fields. Journal de Théorie des Nombres de Bordeaux, Tome 5 (1993) no. 1, pp. 165-178. http://www.numdam.org/item/JTNB_1993__5_1_165_0/

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