Cohomology groups of units in ℤ p d -extensions

Mingzhi Xu

Acta Arithmetica (1998)

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

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Mingzhi 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

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  1. [1] J. W. S. Cassels and A. Fröhlich (eds.), Algebraic Number Theory, Academic Press, 1967. 
  2. [2] R. Greenberg, The Iwasawa invariants of Γ-extensions of a fixed number field, Amer. J. Math. 95 (1973), 204-214. Zbl0268.12005
  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] K. Iwasawa, On cohomology groups of units for Z p -extensions, Amer. J. Math. 105 (1983), 189-200. Zbl0525.12009
  6. [6] S. Lang, Cyclotomic Fields, I and II, Springer, 1990. Zbl0704.11038
  7. [7] H. Matsumura, Commutative Algebra, Math. Lecture Note Ser. 56, Benjamin// Cummings, 1980. 
  8. [8] P. Monsky, On p-adic power series, Math. Ann. 255 (1981), 217-227. Zbl0437.12016
  9. [9] K. Rubin, The 'main conjecture' of Iwasawa theory for imaginary quadratic fields, Invent. Math. 103 (1991), 25-68. Zbl0737.11030
  10. [10] S. Shatz, Profinite Groups, Arithmetic, and Geometry, Princeton Univ. Press, 1972. Zbl0236.12002
  11. [11] L. Washington, Introduction to Cyclotomic Fields, Springer, 1982. Zbl0484.12001
  12. [12] J.-P. Wintenberger, Structure galoisienne de limites projectives d'unités locales, Compositio Math. 42 (1981), 89-103. Zbl0414.12008

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