Local Class Field Theory via Lubin-Tate Theory

Teruyoshi Yoshida[1]

  • [1] Harvard University, Department of Mathematics, 1 Oxford Street, Cambridge, MA 02138, USA

Annales de la faculté des sciences de Toulouse Mathématiques (2008)

  • Volume: 17, Issue: 2, page 411-438
  • ISSN: 0240-2963

Abstract

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We give a self-contained exposition of local class field theory, via Lubin-Tate theory and the Hasse-Arf theorem, refining the arguments of Iwasawa [9].

How to cite

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Yoshida, Teruyoshi. "Local Class Field Theory via Lubin-Tate Theory." Annales de la faculté des sciences de Toulouse Mathématiques 17.2 (2008): 411-438. <http://eudml.org/doc/10091>.

@article{Yoshida2008,
abstract = {We give a self-contained exposition of local class field theory, via Lubin-Tate theory and the Hasse-Arf theorem, refining the arguments of Iwasawa [9].},
affiliation = {Harvard University, Department of Mathematics, 1 Oxford Street, Cambridge, MA 02138, USA},
author = {Yoshida, Teruyoshi},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {Local class field theory; Lubin-Tate formal group laws; Coleman norm operator},
language = {eng},
month = {6},
number = {2},
pages = {411-438},
publisher = {Université Paul Sabatier, Toulouse},
title = {Local Class Field Theory via Lubin-Tate Theory},
url = {http://eudml.org/doc/10091},
volume = {17},
year = {2008},
}

TY - JOUR
AU - Yoshida, Teruyoshi
TI - Local Class Field Theory via Lubin-Tate Theory
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2008/6//
PB - Université Paul Sabatier, Toulouse
VL - 17
IS - 2
SP - 411
EP - 438
AB - We give a self-contained exposition of local class field theory, via Lubin-Tate theory and the Hasse-Arf theorem, refining the arguments of Iwasawa [9].
LA - eng
KW - Local class field theory; Lubin-Tate formal group laws; Coleman norm operator
UR - http://eudml.org/doc/10091
ER -

References

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  2. Carayol (H.).— Non-abelian Lubin-Tate theory, in : Automorphic Forms, Shimura Varieties, and L-functions (Academic Press, 1990), p. 15-39. Zbl0704.11049MR1044827
  3. Cassels (J.W.S.).— Local Fields, London Mathematical Society Student Texts 3, Cambridge Univ. Press, (1986). Zbl0595.12006MR861410
  4. Coleman (R.).— Division values in local fields, Invent. Math. 53, p. 91-116 (1979). Zbl0429.12010MR560409
  5. de Shalit (E.).— Relative Lubin-Tate groups, Proc. Amer. Math. Soc. 95, p. 1-4 (1985). Zbl0578.12013MR796434
  6. Fesenko (I.B.), Vostokov (S.V.).— Local Fields and their Extensions, 2nd ed., Translations of Mathematical Monographs 121, AMS, (2002). Zbl1156.11046MR1915966
  7. Gold (R.).— Local class field theory via Lubin-Tate groups, Indiana Univ. Math. J. 30, p. 795-798 (1981). Zbl0596.12014MR625603
  8. Hazewinkel (M.).— Local class field theory is easy, Advances in Math. 18-2, p. 148-181 (1975). Zbl0312.12022MR389858
  9. Iwasawa (K.).— Local Class Field Theory, Oxford Univ. Press, (1986). Zbl0604.12014MR863740
  10. Lubin (J.).— The local Kronecker-Weber theorem, Trans. Amer. Math. Soc. 267-1, p. 133-138 (1981). Zbl0476.12014MR621978
  11. Lubin (J.), Tate (J.).— Formal complex multiplication in local fields, Ann. Math. 81, p. 380-387 (1965). Zbl0128.26501MR172878
  12. Neukirch (J.).— Class Field Theory, Grundlehren der Mathematischen Wissenschaften 280, Springer-Verlag, (1986). Zbl0587.12001MR819231
  13. Rosen (M.).— An elementary proof of the Kronecker-Weber theorem, Trans. Amer. Math. Soc. 265-2, p. 599-605. (1981) Zbl0474.12014MR610968
  14. Sen (S.).— On automorphisms of local fields, Ann. Math. 90 (1969), p. 33-46. Zbl0199.36301MR244214
  15. Serre (J.-P.).— Corps Locaux, 2nd ed., Hermann, 1968. (English translation : Local fields, Graduate Texts in Mathematics 67, Springer-Verlag, (1979).) Zbl0137.02601MR354618
  16. Serre (J.-P.).— Local class field theory, in : Algebraic Number Theory (Thompson, 1967), p. 128-161. MR220701

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