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

Manabu Ozaki

Acta Arithmetica (1997)

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

How to cite

top

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

top
  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 ℤ 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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.