Classes d'idéaux et classes de diviseurs

Lang, Serge

Lang, Serge

Séminaire Delange-Pisot-Poitou. Théorie des nombres, Tome 18 (1976-1977) no. 2, Exposé no. 28, 9 p.

Zbl

@article{SDPP_1976-1977__18_2_A9_0,
     author = {Lang, Serge},
     title = {Classes d'id\'eaux et classes de diviseurs},
     journal = {S\'eminaire Delange-Pisot-Poitou. Th\'eorie des nombres},
     note = {talk:28},
     pages = {1--9},
     publisher = {Secr\'etariat math\'ematique},
     volume = {18},
     number = {2},
     year = {1976-1977},
     zbl = {0371.12022},
     language = {fr},
     url = {http://archive.numdam.org/item/SDPP_1976-1977__18_2_A9_0/}
}

TY  - JOUR
AU  - Lang, Serge
TI  - Classes d'idéaux et classes de diviseurs
JO  - Séminaire Delange-Pisot-Poitou. Théorie des nombres
N1  - talk:28
PY  - 1976-1977
SP  - 1
EP  - 9
VL  - 18
IS  - 2
PB  - Secrétariat mathématique
UR  - http://archive.numdam.org/item/SDPP_1976-1977__18_2_A9_0/
LA  - fr
ID  - SDPP_1976-1977__18_2_A9_0
ER  -

%0 Journal Article
%A Lang, Serge
%T Classes d'idéaux et classes de diviseurs
%J Séminaire Delange-Pisot-Poitou. Théorie des nombres
%Z talk:28
%D 1976-1977
%P 1-9
%V 18
%N 2
%I Secrétariat mathématique
%U http://archive.numdam.org/item/SDPP_1976-1977__18_2_A9_0/
%G fr
%F SDPP_1976-1977__18_2_A9_0

Lang, Serge. Classes d'idéaux et classes de diviseurs. Séminaire Delange-Pisot-Poitou. Théorie des nombres, Tome 18 (1976-1977) no. 2, Exposé no. 28, 9 p. http://archive.numdam.org/item/SDPP_1976-1977__18_2_A9_0/

Bibliographie
Cité par

[Co 1] Coates (J.). - On K2 and some classical conjectures in algebraic number theory, Annals of Math., t. 95, 1972, p. 99-116. | MR | Zbl

[Co 2] Coates (J.). - K-theory and Iwasawa's analogue of the jacobian, "Algebraic K-theory, II", p. 502-520. - Berlin, Springer-Verlag, 1973 (Lecture Notes in Mathematics, 342). | MR | Zbl

[Co 3] Coates (J.). - p-adic L-functions and Iwasawa's theory, "Conference on algebraic number theory and class field theory" [1976. Tokyo].

[Co 4] Coates (J.). - Fonctions zéta partielles d'un corps de nombres totalement réel, Séminaire Delange-Pisot-Poitou : Théorie des nombres, 16e année, 1974/75, n° 1, 9 p. | Numdam | Zbl

[C-L] Coates (J.) and Lichtenbaum (S.). - On l-adic zeta functions, Annals of Math., t. 98, 1973, p. 498-550. | MR | Zbl

[C-S 1] Coates (J.) and Sinnott (W.). - On p-adic L-functions over real quadratic fields, Invent. Math., Berlin, t. 25, 1974, p. 253-279. | MR | Zbl

[C-S 2] Coates (J.) and Sinnott (W.). - An analogue of Stickelberger's theorem for higher K-groups, Invent. Math., Berlin, t. 24, 1974, p. 149-161. | MR | Zbl

[C-S 3] Coates (J.) and Sinnott (W.). - Integrality properties of the values of partial zeta functions, Proc. London math. Soc., t. 34, 1977, p. 365-384. | MR | Zbl

[C-W 1] Coates (J.) and Wiles (A.). - Explicit reciprocity laws, "Journées arithmétiques de Caen [1976. Caen]", Astérisque, 1977, p. 7. | Numdam | MR | Zbl

[C-W 2] Coates (J.) and Wiles (A.). - On the conjecture of Birch and Swinnerton-Dyer, Invent. Math., Berlin, t. 39, 1977, p. 223-251. | MR | Zbl

[C-W 3] Coates (J.) and Wiles (A.). - Kummer's criterion for Hurwitz numbers (à paraître). | Zbl

[Iw 1] Iwasawa (K.). - On Γ-extensions of algebraic number fields, Bull. Amer. math. Soc., t. 65, 1959, p. 183-226. | Zbl

[Iw 2] Iwasawa (K.). - A note on the group of units of an algebraic number field, J. Math. pures et appl., t. 35, 1956, p. 189-192. | MR | Zbl

[Iw 3] Iwasawa (K.). - Sheaves for algebraic number fields, Annals of Math., t. 69, 1959, p. 408-413. | MR | Zbl

[Iw 4] Iwasawa (K.). - On some properties of Γ-finite modules, Annals of Math., t. 70, 1959, p. 291-312. | Zbl

[Iw 5] Iwasawa (K.). - On the theory of cyclotomic fields, Annals of Math., t. 70, 1959, p. 530-561. | MR | Zbl

[Iw 6] Iwasawa (K.). - On some invariants of cyclotomic fields, Amer. J. Math., t. 80, 1958, p. 773-783. | MR | Zbl

[Iw 7] Iwasawa (K.). - A class number formula for cyclotomic fields, Annals of Math., t. 76, 1962, p. 171-179. | MR | Zbl

[Iw 8] Iwasawa (K.). - On some modules in the theory of cyclotomic fields, J. Math. Soc. Japan, t. 16, 1964, p. 42-82. | MR | Zbl

[Iw 9] Iwasawa (K.). - Some results in the theory of cyclotomic fields, "Theory of numbers", p. 66-69. - Providence. American mathematical Society, 1965 (Proceedings of Symposia in pure Mathematics, 8). | MR | Zbl

[Iw 10] Iwasawa (K.). - On explicit formulas for the norm residue symbol, J. Math. Soc. Japan, t. 20, 1968, p. 151-165. | MR | Zbl

[Iw 11] Iwasawa (K.). - On p-adic L-functions, Annals of Math., t. 89, 1969, p. 198-205. | MR | Zbl

[Iw 12] Iwasawa (K.). - On Zl-extensions of algebraic number fields, Annals of Math., t. 98, 1973, p. 246-326. | MR | Zbl

[Iw 13] Iwasawa (K.). - A note on cyclotomic fields, Invent. Math., Berlin, t. 36, 1976, p. 115-123. | MR | Zbl

[Iw 14] Iwasawa (K.). - Lectures on p-adic L-functions. - Princeton, Princeton University Press, 1972 (Annals of Mathematics Studies, 74). | MR | Zbl

[KL 1] Kubert (D.) and Lang (S.).-Units in the modular function field, I, Math. Annalen, t. 218, 1975, p. 67-96. | MR | Zbl

[KL 2] Kubert (D.) and Lang (S. ). - Units in the modular function field, II, Math. Annalen, t. 218, 1975, p. 175-189. | MR | Zbl

[KL 3] Kubert (D.) and Lang (S.). - Units in the modular function field, III, Math. Annalen, t. 218, 1975, p. 273-285. | MR | Zbl

[KL 4] Kubert (D.) and Lang (S.). - Units in the modular function field, IV, Math. Annalen, t. 227, 1977, p. 223-242. | MR | Zbl

[KL 5] Kubert (D.) and Lang (S.). - Distributions on toroidal groups, Math. Z., t. 148, 1976, p. 33-51. | MR | Zbl

[KL 6] Kubert (D.) and Lang (S.). - The p-primary component of the cuspidal divisor class group on the modular curve X(p) , Math. Annalen (à paraître). | Zbl

[KL 7] Kubert (D.) and Lang (S.). - The index of Stickelberger ideals of order 2 and cuspidal class numbers (à paraître). | Zbl

[KL 8] Kubert (D.) and Lang ( S. ) . - Stickelberger ideals (à paraître).

[KL 9] Kubert (D.) and Lang (S.). - Iwasawa theory in the modular tower (à paraître).

[Ku-L] Kubota (T.) and Leopoldt (H.). - Eine p-adische Theorie der Zetawerte, J. für reine und angew. Math., t. 214/215, 1964, p. 328-339. | MR | Zbl

[L 1] Lang (S.). - Algebraic numbet theory. - Reading, Addison-Wesley publishing Company, 1970. | MR | Zbl

[L 2] Lang (S.). - Elliptic functions. - Reading, Addison-Wesley publishing Company, 1973. | MR | Zbl

[L 3] Lang (S.). - Introduction to modular forms. - Berlin, Springer-Verlag, 1976 (Grundlehren der mathematischen Wissenschaften, 222). | MR | Zbl

[L 4] Lang (S. ). - Introduction to cyclotomic fields (à paraître).

[Le 1] Leopoldt (H.W.). - Zur Geschlechtertheorie in abelschen Zahlkörpern, Math. Nach., t. 9, 1953, p. 351-362. | MR | Zbl

[Le 2] Leopoldt (H.W.). - Über Einheitengruppe und Klassenzahl reeller Zahlkörper, Abh. Deutschen Akad. Wiss. Berlin, Kl. Math., 1953, n° 2, 48 p. | MR | Zbl

[Le 3] Leopoldt (H.W.). - Über ein Fundamentalproblem der Theorie der Einheiten algebraischer Zahlkörper, Sitzungsb. bayerischen Akademie Wiss., 1956, p. 41-48. | MR | Zbl

[Le 4] Leopoldt (H.W.). - Eine Verallgemeinerung der Bernoullischen Zahlen, Abh. Math. Sem. Hamburg, t. 22, 1958, p. 131-140. | MR | Zbl

[Le 5] Leopoldt (H.W.). - Zur Struktur der l-Klassengruppe galoisscher Zahlkörper, J. für reine und angew. Math., t. 199, 1958, p. 165-174. | MR | Zbl

[Le 6] Leopoldt (H.W.). - Über Klassenzahlprimteiler reeller abelscher Zahlkörper ..., Abh. Math. Sem. Hamburg, t. 23, 1959, p. 36- 47. | MR | Zbl

[Le 7] Leopoldt (H.W.). - Über die Hauptordnung der ganzen Elemente eines abelschen Zahlkörpers, J. für reine und angew. Math., t. 201, 1959,p. 119-149. | MR | Zbl

[Le 8] Leopoldt (H.W.). - Über Fermatquotienten von Kreiseinheiten und Klassenzahlformeln modulo p , Rend. Circ. Mat. Palermo, t. 9, 1960, p. 39-50. | MR | Zbl

[Le 9] Leopoldt (H.W.). - Zur Approximation des p-adischen Logarithmus, Abh. Math. Sem. Hamburg, t. 25, 1961, p. 77-81. | MR | Zbl

[Le 10] Leopoldt (H.W.). - Zur Arithmetik in abelschen Zahikörpern, J. für reine und angew. Math., t. 209, 1962, p. 54-71. | MR | Zbl

[Li] Lichtenbaum (S. ). - Values of zeta functions, etale cohomology, and algebraic K-theory, "Algebraic K-theory, II", p. 489-501. - Berlin, Springer-Verlag, 1973 (Lecture Notes in Mathematics, 342). | MR | Zbl

[Lu] Lubin (J.). - One parameter formal Lie groups over p-adic integer rings, Annals of Math., t. 80, 1964, p. 464-484. | MR | Zbl

[L-T] Lubin (J.) and Tate (J.). - Formal complex multiplication in local fields, Annals of Math., t. 8, 1965, p. 380-387. | MR | Zbl

[No] Novikov (A.P.). - Sur le nombre de classes des extensions abéliennes d'un corps quadratique imaginaire [en russe], Izv. Akad. Nauk SSSR, Ser. Mat., t. 31, 1967, p. 717-726.

[Mi] Milnor (J. ). - Introduction to algebraic K-theory. - Princeton, Princeton University Press, 1971 (Annals of Mathematics Studies, 72). | MR | Zbl

[Qu 1] Quillen ( D. ) . - Finite generation of the groups Ki of rings of algebraic integers, "Algebraic K-theory, I", p. 179-198. - Berlin, Springer-Verlag, 1973 (Lecture Notes in Mathematics, 341). | MR | Zbl

[Qu 2] Quillen (D.). - Higher algebraic K-theory I, "Algebraic K-theory, I", p. 85-147. - Berlin, Springer-Verlag, 1973 (Lecture Notes in Mathematics, 341). | MR | Zbl

[Ri] Ribet (K.). - A modular construction of unramified p-extensions of Q(μp) , Invent. Math., Berlin, t. 34, 1976, p. 151-162. | Zbl

[Rob] Robert ( G. ) . - Nombres de Hurwitz et unités elliptiques (à paraître).

[Roh] Rohrlich ( D. ) . - Modular functions and the Fermat curve, Invent. Math., Berlin, 1977 (à paraître).

[Se 1] Serre (J.-P.). - Classes des corps cyclotomiques, d'après Iwasawa, Séminaire Bourbaki, 11e année, 1958/59, n° 174, 11 p. | Numdam | Zbl

[Se 2] Serre (J.-P.). - Formes modulaires et fonctions zeta p-adiques, "Modular functions of one variable, III", p. 191-268. - Berlin, Springer-Verlag, 1973 (Lecture Notes in Mathematics, 350). | MR | Zbl

[Si] Siegel (C.L.). - Über die Fourierschen Koeffizienten von Modulformen, Göttingen Nachrichten, t. 3, 1970, p. 15-56. | MR | Zbl

[Si] Sinnott (W.). - The index of the Stickelberger ideal (à paraître).

[St] Stark (H.). - L-functions at s = 1 , III : Totally real fields and Hilbert's twelfth problem (à paraître). | Zbl

[Ta 1] Tate (J. ). - Letter to Iwasawa on a relation between K2 and Galois cohomology, "Algebraic K-theory, II", p. 524-527. - Berlin, Springer-Verlag, 1973 (Lecture Notes in Mathematics, 342). | MR | Zbl

[Ta 2] Tate (J.). - Relations between K2 and Galois cohomology, Invent. Math., Berlin, t. 36, 1976, p. 257-274. | MR | Zbl

[Ta 3] Tate (J.). - Symbols in arithmetic, "Actes du Congrès international des Mathématiciens [1970. Nice]", Tome 1, p. 201-211. - Paris, Gauthier-Villars, 1971. | MR | Zbl