Cohomology groups of units in $ℤ^d_p$-extensions

• Autorzy: Mingzhi Xu
• Języki publikacji: EN

Kategorie tematyczne

• 14H25: Arithmetic ground fields
• 14G10: Zeta-functions and related questions (Birch-Swinnerton-Dyer conjecture)
• 14G25: Global ground fields

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1998
• Tom: 86
• Numer: 4
• Strony: 289-304

Daty

wydano

1998

otrzymano

1997-07-15

poprawiono

1998-05-05

Twórcy

autor

Mingzhi Xu

• Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, Ohio 43210, U.S.A.

Bibliografia

• [1] J. W. S. Cassels and A. Fröhlich (eds.), Algebraic Number Theory, Academic Press, 1967.
• [2] R. Greenberg, The Iwasawa invariants of Γ-extensions of a fixed number field, Amer. J. Math. 95 (1973), 204-214.
• [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] K. Iwasawa, On cohomology groups of units for $Z_p$-extensions, Amer. J. Math. 105 (1983), 189-200.
• [6] S. Lang, Cyclotomic Fields, I and II, Springer, 1990.
• [7] H. Matsumura, Commutative Algebra, Math. Lecture Note Ser. 56, Benjamin// Cummings, 1980.
• [8] P. Monsky, On p-adic power series, Math. Ann. 255 (1981), 217-227.
• [9] K. Rubin, The 'main conjecture' of Iwasawa theory for imaginary quadratic fields, Invent. Math. 103 (1991), 25-68.
• [10] S. Shatz, Profinite Groups, Arithmetic, and Geometry, Princeton Univ. Press, 1972.
• [11] L. Washington, Introduction to Cyclotomic Fields, Springer, 1982.
• [12] J.-P. Wintenberger, Structure galoisienne de limites projectives d'unités locales, Compositio Math. 42 (1981), 89-103.