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Teruyoshi Yoshida
Local Class Field Theory via Lubin-Tate Theory
Annales de la faculté des sciences de Toulouse Sér. 6, 17 no. 2 (2008), p. 411-438
Article: subscription required | Reviews MR 2487860 | Zbl pre05503161
[1] Atiyah (M.F.), Macdonald (I.G.).— Introduction to commutative algebra, Addison-Wesley, (1969). MR 242802 | Zbl 0175.03601
[2] Carayol (H.).— Non-abelian Lubin-Tate theory, in : Automorphic Forms, Shimura Varieties, and L-functions (Academic Press, 1990), p. 15-39. MR 1044827 | Zbl 0704.11049
[3] Cassels (J.W.S.).— Local Fields, London Mathematical Society Student Texts 3, Cambridge Univ. Press, (1986). MR 861410 | Zbl 0595.12006
[4] Coleman (R.).— Division values in local fields, Invent. Math. 53, p. 91-116 (1979).
Article | MR 560409 | Zbl 0429.12010
[5] de Shalit (E.).— Relative Lubin-Tate groups, Proc. Amer. Math. Soc. 95, p. 1-4 (1985). MR 796434 | Zbl 0578.12013
[6] Fesenko (I.B.), Vostokov (S.V.).— Local Fields and their Extensions, 2nd ed., Translations of Mathematical Monographs 121, AMS, (2002). MR 1915966 | Zbl pre01793794
[7] Gold (R.).— Local class field theory via Lubin-Tate groups, Indiana Univ. Math. J. 30, p. 795-798 (1981). MR 625603 | Zbl 0596.12014
[8] Hazewinkel (M.).— Local class field theory is easy, Advances in Math. 18-2, p. 148-181 (1975). MR 389858 | Zbl 0312.12022
[9] Iwasawa (K.).— Local Class Field Theory, Oxford Univ. Press, (1986). MR 863740 | Zbl 0604.12014
[10] Lubin (J.).— The local Kronecker-Weber theorem, Trans. Amer. Math. Soc. 267-1, p. 133-138 (1981). MR 621978 | Zbl 0476.12014
[11] Lubin (J.), Tate (J.).— Formal complex multiplication in local fields, Ann. Math. 81, p. 380-387 (1965). MR 172878 | Zbl 0128.26501
[12] Neukirch (J.).— Class Field Theory, Grundlehren der Mathematischen Wissenschaften 280, Springer-Verlag, (1986). MR 819231 | Zbl 0587.12001
[13] Rosen (M.).— An elementary proof of the Kronecker-Weber theorem, Trans. Amer. Math. Soc. 265-2, p. 599-605. (1981) MR 610968 | Zbl 0474.12014
[14] Sen (S.).— On automorphisms of local fields, Ann. Math. 90 (1969), p. 33-46. MR 244214 | Zbl 0199.36301
[15] Serre (J.-P.).— Corps Locaux, 2nd ed., Hermann, 1968. (English translation : Local fields, Graduate Texts in Mathematics 67, Springer-Verlag, (1979).) MR 354618 | Zbl 0137.02601
[16] Serre (J.-P.).— Local class field theory, in : Algebraic Number Theory (Thompson, 1967), p. 128-161. MR 220701
Teruyoshi Yoshida
Local Class Field Theory via Lubin-Tate Theory
Annales de la faculté des sciences de Toulouse Sér. 6, 17 no. 2 (2008), p. 411-438
Article: subscription required | Reviews MR 2487860 | Zbl pre05503161
Résumé - 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].
Bibliography
[2] Carayol (H.).— Non-abelian Lubin-Tate theory, in : Automorphic Forms, Shimura Varieties, and L-functions (Academic Press, 1990), p. 15-39. MR 1044827 | Zbl 0704.11049
[3] Cassels (J.W.S.).— Local Fields, London Mathematical Society Student Texts 3, Cambridge Univ. Press, (1986). MR 861410 | Zbl 0595.12006
[4] Coleman (R.).— Division values in local fields, Invent. Math. 53, p. 91-116 (1979).
Article | MR 560409 | Zbl 0429.12010
[5] de Shalit (E.).— Relative Lubin-Tate groups, Proc. Amer. Math. Soc. 95, p. 1-4 (1985). MR 796434 | Zbl 0578.12013
[6] Fesenko (I.B.), Vostokov (S.V.).— Local Fields and their Extensions, 2nd ed., Translations of Mathematical Monographs 121, AMS, (2002). MR 1915966 | Zbl pre01793794
[7] Gold (R.).— Local class field theory via Lubin-Tate groups, Indiana Univ. Math. J. 30, p. 795-798 (1981). MR 625603 | Zbl 0596.12014
[8] Hazewinkel (M.).— Local class field theory is easy, Advances in Math. 18-2, p. 148-181 (1975). MR 389858 | Zbl 0312.12022
[9] Iwasawa (K.).— Local Class Field Theory, Oxford Univ. Press, (1986). MR 863740 | Zbl 0604.12014
[10] Lubin (J.).— The local Kronecker-Weber theorem, Trans. Amer. Math. Soc. 267-1, p. 133-138 (1981). MR 621978 | Zbl 0476.12014
[11] Lubin (J.), Tate (J.).— Formal complex multiplication in local fields, Ann. Math. 81, p. 380-387 (1965). MR 172878 | Zbl 0128.26501
[12] Neukirch (J.).— Class Field Theory, Grundlehren der Mathematischen Wissenschaften 280, Springer-Verlag, (1986). MR 819231 | Zbl 0587.12001
[13] Rosen (M.).— An elementary proof of the Kronecker-Weber theorem, Trans. Amer. Math. Soc. 265-2, p. 599-605. (1981) MR 610968 | Zbl 0474.12014
[14] Sen (S.).— On automorphisms of local fields, Ann. Math. 90 (1969), p. 33-46. MR 244214 | Zbl 0199.36301
[15] Serre (J.-P.).— Corps Locaux, 2nd ed., Hermann, 1968. (English translation : Local fields, Graduate Texts in Mathematics 67, Springer-Verlag, (1979).) MR 354618 | Zbl 0137.02601
[16] Serre (J.-P.).— Local class field theory, in : Algebraic Number Theory (Thompson, 1967), p. 128-161. MR 220701
