Nilpotent local class field theory

Helmut Koch; Susanne Kukkuk; John Labute

Acta Arithmetica (1998)

  • Volume: 83, Issue: 1, page 45-64
  • ISSN: 0065-1036

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Helmut Koch, Susanne Kukkuk, and John Labute. "Nilpotent local class field theory." Acta Arithmetica 83.1 (1998): 45-64. <http://eudml.org/doc/207105>.

@article{HelmutKoch1998,
author = {Helmut Koch, Susanne Kukkuk, John Labute},
journal = {Acta Arithmetica},
keywords = {Artin map; profinite completion; multiplicative group; local field; Galois group; Artin isomorphism; kernel},
language = {eng},
number = {1},
pages = {45-64},
title = {Nilpotent local class field theory},
url = {http://eudml.org/doc/207105},
volume = {83},
year = {1998},
}

TY - JOUR
AU - Helmut Koch
AU - Susanne Kukkuk
AU - John Labute
TI - Nilpotent local class field theory
JO - Acta Arithmetica
PY - 1998
VL - 83
IS - 1
SP - 45
EP - 64
LA - eng
KW - Artin map; profinite completion; multiplicative group; local field; Galois group; Artin isomorphism; kernel
UR - http://eudml.org/doc/207105
ER -

References

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  3. [Ka] M. Kaufhold, Zur Verzweigungsgruppenfiltrierung auf dem zweiten Zentralschritt lokaler Galoisgruppen, Dissertation, Berlin, 1993. 
  4. [Ko1] H. Koch, Galoissche Theorie der p-Erweiterungen, Springer, Berlin, 1970. 
  5. [Ko2] H. Koch, Über Galoissche Gruppen von p-adischen Zahlkörpern, Math. Nachr. 35 (1967), 323-327. 
  6. [Ku] S. Kukkuk, Graduierte nilpotente Klassenkörpertheorie, Dissertation, Berlin, 1995. 
  7. [La0] J. P. Labute, Classification of Demushkin groups, Canad. J. Math. 19 (1966), 106-132. 
  8. [La1] J. P. Labute, Algèbres de Lie et pro-p-groupes définis par une seule relation, Invent. Math. 4 (1967), 142-158. Zbl0212.36303
  9. [La2] J. P. Labute, On the descending central series of groups with a single defining relation, J Algebra 14 (1970), 16-23. Zbl0198.34601
  10. [La3] J. P. Labute, The lower central series of the group ⟨ x , y : x p = 1 ⟩ , Proc. Amer. Math. Soc. 66 (1977), 197-201. 
  11. [La4] J. P. Labute, Free Lie algebras as modules over their enveloping algebras, Proc. Amer. Math. Soc. 68 (1978), 135-139. Zbl0379.17004
  12. [Lz] M. Lazard, Groupes analytiques p-adiques, IHES Publ. Math. 26 (1965), 389-603. Zbl0139.02302
  13. [Se1] J.-P. Serre, Lie Algebras and Lie Groups, Lecture Notes in Math. 1500, Springer, Berlin, 1991. 
  14. [Se2] J.-P. Serre, Cohomologie Galoisienne, Springer, Berlin, 1973. 
  15. [Sk] A. I. Skopin, The factor groups of a descending central series, Dokl. Akad. Nauk SSSR 74 (1950), 425-428 (in Russian). 
  16. [We] A. Weil, Basic Number Theory, Springer, Berlin, 1967. 
  17. [Wi1] E. Witt, Treue Darstellung Liescher Ringe, J. Reine Angew. Math. 177 (1937), 152-160. 
  18. [Wi2] E. Witt, Die Unterringe der freien Lieschen Ringe, Math. Z. 64 (1956), 195-216. Zbl0070.02903
  19. [Zi1] E.-W. Zink, Lokale projektive Klassenkörpertheorie, Grundbegriffe und erste Resultate, Akad. Wiss. DDR, R-Math-01/82, Berlin, 1982. 
  20. [Zi2] E.-W. Zink, Lokale projektive Klassenkörpertheorie, II, Math. Nachr. 114 (1983), 123-150. Zbl0547.12012

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