Fitting ideals of class groups in a p -extension

Pietro Cornacchia

Acta Arithmetica (1998)

  • Volume: 87, Issue: 1, page 79-88
  • ISSN: 0065-1036

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Pietro Cornacchia. "Fitting ideals of class groups in a $ℤ_p$-extension." Acta Arithmetica 87.1 (1998): 79-88. <http://eudml.org/doc/207206>.

@article{PietroCornacchia1998,
author = {Pietro Cornacchia},
journal = {Acta Arithmetica},
keywords = {-extension; Tate cohomology group; ideal class group; Iwasawa algebra; Fitting ideal},
language = {eng},
number = {1},
pages = {79-88},
title = {Fitting ideals of class groups in a $ℤ_p$-extension},
url = {http://eudml.org/doc/207206},
volume = {87},
year = {1998},
}

TY - JOUR
AU - Pietro Cornacchia
TI - Fitting ideals of class groups in a $ℤ_p$-extension
JO - Acta Arithmetica
PY - 1998
VL - 87
IS - 1
SP - 79
EP - 88
LA - eng
KW - -extension; Tate cohomology group; ideal class group; Iwasawa algebra; Fitting ideal
UR - http://eudml.org/doc/207206
ER -

References

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  1. [1] N. Bourbaki, Algebra I, Springer, New York, 1989. 
  2. [2] J. W. S. Cassels and A. Fröhlich, Algebraic Number Theory, Academic Press, London, 1967. Zbl0153.07403
  3. [3] P. Cornacchia, Anderson's module for cyclotomic fields of prime conductor, J. Number Theory 67 (1997), 252-276. Zbl0888.11045
  4. [4] P. Cornacchia and C. Greither, Fitting ideals of class groups of real fields of prime power conductor, J. Number Theory, to appear. 
  5. [5] M. Grandet et J.-F. Jaulent, Sur la capitulation dans une l -extension, J. Reine Angew. Math. 362 (1985), 213-217. Zbl0564.12011
  6. [6] R. Greenberg, On the Iwasawa invariants of totally real number fields, Amer. J. Math. 98 (1976), 263-284. Zbl0334.12013
  7. [7] C. Greither, Class groups of abelian fields, and the main conjecture, Ann. Inst. Fourier (Grenoble) 42 (1992), no. 3, 449-499. Zbl0729.11053
  8. [8] C. Greither, The structure of some minus class groups, and Chinburg's third conjecture for abelian fields, Math. Z., to appear. Zbl0919.11072
  9. [9] K. Iwasawa, On l -extensions of algebraic number fields, Ann. of Math. (2) 98 (1973), 246-326. 
  10. [10] J. M. Kim, S. Bae and I.-S. Lee, Cyclotomic units in p -extensions, Israel J. Math. 75 (1991), 161-165. Zbl0765.11042
  11. [11] J. S. Kraft and R. Schoof, Computing Iwasawa modules of real quadratic number fields, Compositio Math. 97 (1995), 135-155. Zbl0840.11043
  12. [12] L. V. Kuz'min, On formulae for the class number of real Abelian fields, Russian Acad. Sci. Izv. Math. 60 (1996), 695-761. 
  13. [13] S. Lang, Cyclotomic Fields I and II, combined 2nd ed., Grad. Texts in Math. 121, Springer, New York, 1990. Zbl0704.11038
  14. [14] B. Mazur and A. Wiles, Class fields of abelian extensions of ℚ, Invent. Math. 76 (1984), 179-330. Zbl0545.12005
  15. [15] M. Ozaki, On the cyclotomic unit group and the ideal class group of a real abelian number field, J. Number Theory 64 (1997), 211-222. Zbl0879.11058
  16. [16] M. Ozaki, On the cyclotomic unit group and the ideal class group of a real abelian number field II, J. Number Theory., 223-232. Zbl0879.11059
  17. [17] K. Rubin, The Main Conjecture, Appendix to [13]. 
  18. [18] R. Schoof, The structure of the minus class groups of abelian number fields, in: Séminaire de Théorie des Nombres, Paris 1988-89, Progr. Math. 91, Birkhäuser, 1991, 185-204. 
  19. [19] W. Sinnott, On the Stickelberger ideal and the circular units of an abelian field, Invent. Math. 62 (1980), 181-234. Zbl0465.12001
  20. [20] L. C. Washington, Introduction to Cyclotomic Fields, 2nd ed., Grad. Texts in Math. 83, Springer, New York, 1997. Zbl0966.11047

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