# Cohomology groups of units in ${\mathbb{Z}}_{p}^{d}$-extensions

Acta Arithmetica (1998)

- Volume: 86, Issue: 4, page 289-304
- ISSN: 0065-1036

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top## How to cite

topMingzhi Xu. "Cohomology groups of units in $ℤ^d_p$-extensions." Acta Arithmetica 86.4 (1998): 289-304. <http://eudml.org/doc/207198>.

@article{MingzhiXu1998,

author = {Mingzhi Xu},

journal = {Acta Arithmetica},

keywords = {cohomology groups of units; heights of ideals; Iwasawa algebra; Leopoldt hypothesis},

language = {eng},

number = {4},

pages = {289-304},

title = {Cohomology groups of units in $ℤ^d_p$-extensions},

url = {http://eudml.org/doc/207198},

volume = {86},

year = {1998},

}

TY - JOUR

AU - Mingzhi Xu

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

JO - Acta Arithmetica

PY - 1998

VL - 86

IS - 4

SP - 289

EP - 304

LA - eng

KW - cohomology groups of units; heights of ideals; Iwasawa algebra; Leopoldt hypothesis

UR - http://eudml.org/doc/207198

ER -

## References

top- [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. Zbl0268.12005
- [3] R. Greenberg, On the structure of certain Galois groups, Invent. Math. 47 (1978), 85-99. Zbl0403.12004
- [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. Zbl0525.12009
- [6] S. Lang, Cyclotomic Fields, I and II, Springer, 1990. Zbl0704.11038
- [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. Zbl0437.12016
- [9] K. Rubin, The 'main conjecture' of Iwasawa theory for imaginary quadratic fields, Invent. Math. 103 (1991), 25-68. Zbl0737.11030
- [10] S. Shatz, Profinite Groups, Arithmetic, and Geometry, Princeton Univ. Press, 1972. Zbl0236.12002
- [11] L. Washington, Introduction to Cyclotomic Fields, Springer, 1982. Zbl0484.12001
- [12] J.-P. Wintenberger, Structure galoisienne de limites projectives d'unités locales, Compositio Math. 42 (1981), 89-103. Zbl0414.12008

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