Remarks on connections between the Leopoldt conjecture, p-class groups and unit groups of algebraic number fields

Hiroshi YAMASHITA

doi:10.2969/jmsj/04220221

Hiroshi YAMASHITA

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JOURNAL FREE ACCESS

1990 Volume 42 Issue 2 Pages 221-237

DOI https://doi.org/10.2969/jmsj/04220221

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Published: 1990 Received: June 18, 1988 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) J. Ax, On the units of an algebraic number field, Illinois J. Math., 9 (1965), 584-589.
2) A. Brumer, On the units of algebraic number fields, Mathematika, 14 (1967), 121-124.
3) R. Gillard, Formulations de la conjecture de Leopoldt et étude d'une condition suffisante, Abh. Math. Sem. Univ. Hamburg, 48 (1979), 125-138.
4) G. Gras, Remarques sur la conjecture de Leopoldt, C. R. Acad. Sci. Paris (A), 274 (1972), 377-380.
5) G. Gras, Groupe de Galois de la p-extension abélienne p-ramifiée maximale d'un corps de nombres, J. Reine Angew. Math., 333 (1982), 86-132.
6) G. Gras, Une interpretétation de la conjecture de Leopoldt, C. R. Acad. Sci. Paris (1), 302 (1986), 607-610.
7) K. Iwasawa, On Leopoldt's conjecture (in Japanese), Seminar Note on Algebraic Number Theory, Surikaiseki-kenkynsho, Kyoto, 1984.
8) H. W. Leopoldt, Zur Arithmetik in abelschen Zahlkörpern, J. Reine. Angew. Math., 209 (1962), 54-71.
9) H. Miki, On the Leopoldt conjecture on the p-adic regulators, J. Number Theory, 26 (1987), 117-128.
10) K. Miyake, On the units of an algebraic number field, J. Math. Soc. Japan, 34 (1982), 515-525.
11) O. Neumann, On p-closed algebraic number fields with restricted ramifications, Math. USSR-Izv., 9 (1975), 243-254.
12) J. W. Sands, Kummer's and Iwasawa's version of Leopoldt's conjecture, Canad. Math. Bull., to appear.
13) J. P. Serre, Cohomologie galoisienne, Lecture Notes in Math., 5, Springer, 1964.

Right : [1] J. Ax, On the units of an algebraic number field, Illinois J. Math., 9 (1965), 584-589.
[2] A. Brumer, On the units of algebraic number fields, Mathematika, 14 (1967), 121-124.
[3] R. Gillard, Formulations de la conjecture de Leopoldt et étude d'une condition suffisante, Abh. Math. Sem. Univ. Hamburg, 48 (1979), 125-138.
[4] G. Gras, Remarques sur la conjecture de Leopoldt, C. R. Acad. Sci. Paris (A), 274 (1972), 377-380.
[5] G. Gras, Groupe de Galois de la p-extension abélienne p-ramifiée maximale d'un corps de nombres, J. Reine Angew. Math., 333 (1982), 86-132.
[6] G. Gras, Une interpretétation de la conjecture de Leopoldt, C. R. Acad. Sci. Paris (1), 302 (1986), 607-610.
[7] K. Iwasawa, On Leopoldt's conjecture (in Japanese), Seminar Note on Algebraic Number Theory, Surikaiseki-kenkyusho, Kyoto, 1984.
[8] H. W. Leopoldt, Zur Arithmetik in abelschen Zahlkörpern, J. Reine. Angew. Math., 209 (1962), 54-71.
[9] H. Miki, On the Leopoldt conjecture on the p-adic regulators, J. Number Theory, 26 (1987), 117-128.
[10] K. Miyake, On the units of an algebraic number field, J. Math. Soc. Japan, 34 (1982), 515-525.
[11] O. Neumann, On p-closed algebraic number fields with restricted ramifications, Math. USSR-Izv., 9 (1975), 243-254.
[12] J. W. Sands, Kummer's and Iwasawa's version of Leopoldt's conjecture, Canad. Math. Bull., to appear.
[13] J. P. Serre, Cohomologie galoisienne, Lecture Notes in Math., 5, Springer, 1964.

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