Kummer’s lemma for p -extensions over totally real number fields

Manabu Ozaki

Acta Arithmetica (1997)

  • Volume: 81, Issue: 1, page 37-44
  • ISSN: 0065-1036

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Manabu Ozaki. "Kummer’s lemma for $ℤ_p$-extensions over totally real number fields." Acta Arithmetica 81.1 (1997): 37-44. <http://eudml.org/doc/207053>.

@article{ManabuOzaki1997,
author = {Manabu Ozaki},
journal = {Acta Arithmetica},
keywords = {cyclotomic extensions; Kummer's lemma; Iwasawa theory; -adic -functions},
language = {eng},
number = {1},
pages = {37-44},
title = {Kummer’s lemma for $ℤ_p$-extensions over totally real number fields},
url = {http://eudml.org/doc/207053},
volume = {81},
year = {1997},
}

TY - JOUR
AU - Manabu Ozaki
TI - Kummer’s lemma for $ℤ_p$-extensions over totally real number fields
JO - Acta Arithmetica
PY - 1997
VL - 81
IS - 1
SP - 37
EP - 44
LA - eng
KW - cyclotomic extensions; Kummer's lemma; Iwasawa theory; -adic -functions
UR - http://eudml.org/doc/207053
ER -

References

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  1. [1] J. Coates, p-adic L-functions and Iwasawa's theory, in: Algebraic Number Fields, Durham Symposium, 1975, A. Fröhlich (ed.), Academic Press, London, 1977, 269-353. 
  2. [2] P. Colmez, Résidu en s = 1 des fonctions zêta p-adiques, Invent. Math. 91 (1988), 371-389. Zbl0651.12010
  3. [3] R. Greenberg, On the structure of certain Galois groups, Invent. Math. 47 (1978), 85-99. Zbl0403.12004
  4. [4] K. Iwasawa, On l -extensions of algebraic number fields, Ann. of Math. 98 (1973), 246-326. 
  5. [5] R. W. K. Odoni, On Gauss sums ( m o d p n ) , Bull. London Math. Soc. 5 (1973), 325-327. Zbl0269.10020
  6. [6] W. Sinnott, On p-adic L-functions and the Riemann-Hurwitz genus formula, Compositio Math. 53 (1984), 3-17. Zbl0545.12011
  7. [7] L. C. Washington, Units of irregular cyclotomic fields, Illinois J. Math. 23 (1979), 635-647. Zbl0427.12004
  8. [8] L. C. Washington, Introduction to Cyclotomic Fields, Grad. Texts in Math. 83, Springer, New York, 1982. 
  9. [9] L. C. Washington, Kummer's lemma for prime power cyclotomic fields, J. Number Theory 40 (1992), 165-173. Zbl0746.11043
  10. [10] A. Wiles, The Iwasawa conjecture for totally real fields, Ann. of Math. 131 (1990), 493-540. Zbl0719.11071

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