Kummer's lemma for $ℤ_p$-extensions over totally real number fields

• Autorzy: Manabu Ozaki
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1997
• Tom: 81
• Numer: 1
• Strony: 37-44

Daty

wydano

1997

otrzymano

1996-01-29

poprawiono

1996-10-08

Twórcy

autor

Manabu Ozaki

• Department of Mathematics, School of Science and Engineering, Waseda University, 3-4-1, Ohkubo Shinjuku-ku, Tokyo, 169 Japan

Bibliografia

• [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] P. Colmez, Résidu en s = 1 des fonctions zêta p-adiques, Invent. Math. 91 (1988), 371-389.
• [3] R. Greenberg, On the structure of certain Galois groups, Invent. Math. 47 (1978), 85-99.
• [4] K. Iwasawa, On $ℤ_l$-extensions of algebraic number fields, Ann. of Math. 98 (1973), 246-326.
• [5] R. W. K. Odoni, On Gauss sums $(mod p^n)$, Bull. London Math. Soc. 5 (1973), 325-327.
• [6] W. Sinnott, On p-adic L-functions and the Riemann-Hurwitz genus formula, Compositio Math. 53 (1984), 3-17.
• [7] L. C. Washington, Units of irregular cyclotomic fields, Illinois J. Math. 23 (1979), 635-647.
• [8] L. C. Washington, Introduction to Cyclotomic Fields, Grad. Texts in Math. 83, Springer, New York, 1982.
• [9] L. C. Washington, Kummer's lemma for prime power cyclotomic fields, J. Number Theory 40 (1992), 165-173.
• [10] A. Wiles, The Iwasawa conjecture for totally real fields, Ann. of Math. 131 (1990), 493-540.