Les nombres de Tamagawa locaux et la conjecture de Bloch et Kato pour les motifs (m) sur un corps abélien
Benois, Denis ; Nguyen Quang Do, Thong
Annales scientifiques de l'École Normale Supérieure, Tome 35 (2002), p. 641-672 / Harvested from Numdam
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     author = {Benois, Denis and Nguyen Quang Do, Thong},
     title = {Les nombres de Tamagawa locaux et la conjecture de Bloch et Kato pour les motifs $\mathbb {Q}(m)$ sur un corps ab\'elien},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {35},
     year = {2002},
     pages = {641-672},
     doi = {10.1016/s0012-9593(02)01104-7},
     mrnumber = {1951439},
     zbl = {01910884},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/ASENS_2002_4_35_5_641_0}
}
Benois, Denis; Nguyen Quang Do, Thong. Les nombres de Tamagawa locaux et la conjecture de Bloch et Kato pour les motifs $\mathbb {Q}(m)$ sur un corps abélien. Annales scientifiques de l'École Normale Supérieure, Tome 35 (2002) pp. 641-672. doi : 10.1016/s0012-9593(02)01104-7. http://gdmltest.u-ga.fr/item/ASENS_2002_4_35_5_641_0/

[1] Banaszak G, Generalization of the Moore exact sequence and the wild kernel for higher K-groups, Compositio Math. 86 (3) (1993) 281-305. | Numdam | MR 1219629 | Zbl 0778.11066

[2] Beilinson A., Polylogarithms and cyclotomic elements, Preprint, 1990.

[3] Belliard J.-R, Nguyen Quang Do T, Formules de classes pour les corps abéliens réels, Ann. Inst. Fourier 51 (4) (2001) 903-937. | Numdam | MR 1849210 | Zbl 1007.11063

[4] Belliard J.-R., Nguyen Quang Do T., Modified circular p-units and annihilation of real classes, prépublication, 2001.

[5] Benois D., Burns D., travail en préparation.

[6] Borel A, Cohomologie de SLn et valeurs de fonctions zêta, Ann. Scuola Norm. Sup. Pisa 417 (1974) 613-636. | Numdam | MR 506168 | Zbl 0382.57027

[7] Bloch S, Kato K, L-functions and Tamagawa numbers of motives, Grothendieck Festschrift 1 (1990) 333-400. | MR 1086888 | Zbl 0768.14001

[8] Burns D, Flach M, Motivic L-functions and Galois module structure, Math. Ann. 305 (1996) 65-102. | MR 1386106 | Zbl 0867.11081

[9] Burns D., Greither C., On the equivariant Tamagawa number conjecture for Tate motives, Preprint, 2000. | MR 1992015

[10] Beilinson A, Macpherson R, Schechtman V, Notes on motivic cohomology, Duke Math. J. 54 (1987) 679-710. | MR 899412 | Zbl 0632.14010

[11] Coleman R, Local units modulo circular units, Proc. Amer. Math. Soc. 89 (1983) 1-7. | MR 706497 | Zbl 0528.12005

[12] Deligne P, Le groupe fondamental de la droite projective moins trois points, in: Galois Groups Over Q, MSRI Publications, 16, Springer, 1989, pp. 79-297. | MR 1012168 | Zbl 0742.14022

[13] Dwyer W.-G, Friedlander E.M, Algebraic and etale K-theory, Trans. Amer. Math. Soc. 292 (1985) 247-280. | MR 805962 | Zbl 0581.14012

[14] Flach M, A generalization of the Cassels-Tate pairing, J. Reine Angew. Math. 412 (1990) 113-127. | MR 1079004 | Zbl 0711.14001

[15] Fontaine J.-M, Sur certains types de représentations p-adiques du groupe de Galois d'un corps local ; construction d'un anneau de Barsotti-Tate, Ann. of Math. 115 (1982) 529-577. | MR 657238 | Zbl 0544.14016

[16] Fontaine J.-M, Le corps des périodes p-adiques, Astérisque 223 (1994) 59-102. | MR 1293971

[17] Fontaine J.-M, Valeurs spéciales de fonctions L des motifs, Séminaire Bourbaki, exposé 751, Astérisque 206 (1992) 205-249. | Numdam | MR 1206069 | Zbl 0799.14006

[18] Fontaine J.-M, Perrin-Riou B, Autour des conjectures de Bloch et Kato ; cohomologie galoisienne et valeurs de fonctions L, in: Motives, Proc. Symp. in Pure Math., 55, 1994, pp. 599-706. | MR 1265546 | Zbl 0821.14013

[19] Gillard R, Unité cyclotomiques, unités semi-locales et Zl-extensions, Ann. Inst. Fourier 29 (1) (1979) 49-79. | Numdam | MR 526777 | Zbl 0387.12002

[20] Greither C, Class groups of abelian fields and the main conjecture, Ann. Inst. Fourier 42 (1992) 449-499. | Numdam | MR 1182638 | Zbl 0729.11053

[21] Gross B.H., On the values of Artin L-functions, Preprint, 1980. | MR 2154331 | Zbl 1169.11050

[22] Huber A., Kings G., Bloch-Kato conjecture and main conjecture of Iwasawa theory for Dirichlet characters, Preprint, 2000. | MR 2002643 | Zbl 1044.11095

[23] Huber A, Wildeshaus J, Classical motivic polylogarithm according to Beilinson and Deligne, Doc. Math. J. DMV3 (1998) 27-133. | MR 1643974 | Zbl 0906.19004

[24] Kahn B, On the Lichtenbaum-Quillen conjecture, in: Algebraic K-theory and Algebraic Topology, NATO Proc. Lake Louise, 407, 1993, pp. 147-166. | MR 1367295 | Zbl 0885.19004

[25] Kato K, Lectures on the approach to Iwasawa theory for Hasse-Weil L-functions via BdR. Part I, in: Lecture Notes in Math., 1553, Springer, 1993, pp. 50-163. | MR 1338860 | Zbl 0815.11051

[26] Kato K., Lectures on the approach to Iwasawa theory for Hasse-Weil L-functions via B d R . Part II, Preprint, 1993. | MR 1338860

[27] Kolster M., Nguyen Quang Do T., Universal distribution lattices for abelian number fields, Preprint, 2000.

[28] Kolster M, Nguyen Quang Do T, Fleckinger V, Twisted S-units, p-adic class number formulas and the Lichtenbaum conjectures, Duke Math. J. 84 (1996) 679-717. | MR 1408541 | Zbl 0863.19003

[29] Kuzmin L.V, On formulae for the class number of real abelian fields, Russian Math. Izv. 60 (4) (1996) 695-761. | MR 1416925 | Zbl 1007.11065

[30] Leopoldt H.-W, Über die Hauptordnung der ganzen Elemente eines abelschen Zahlkörpers, J. Reine Angew. Math. 201 (1959) 119-149. | MR 108479 | Zbl 0098.03403

[31] Lettl G, Relative Galois module structure of integers of local abelian fields, Acta Arithmetica 85 (3) (1998) 235-247. | MR 1627831 | Zbl 0910.11050

[32] Milne J.S, Arithmetic Duality Theorems, Perspectives in Mathematics, 1, Academic Press, Boston, 1986. | MR 881804 | Zbl 0613.14019

[33] Neukirch J, The Beilinson conjecture for algebraic number fields, in: Beilinson's Conjectures on Special Values of L-functions, Perspectives in Math., 4, Academic Press, 1988, pp. 193-247. | MR 944995 | Zbl 0651.12009

[34] Nguyen Quang Do T, Analogues supérieurs du noyau sauvage, J. Théorie des Nombres Bordeaux 4 (1992) 263-271. | Numdam | MR 1208865 | Zbl 0783.11042

[35] Perrin-Riou B, Théorie d'Iwasawa des représentations p-adiques sur un corps local, Invent. Math. 115 (1994) 81-149. | MR 1248080 | Zbl 0838.11071

[36] Perrin-Riou B, Fonctions L p-adiques, in: Proc. Int. Congress of Math., Birkhäuser Verlag, Zürich, 1995, pp. 400-410. | MR 1403940 | Zbl 0853.11093

[37] Perrin-Riou B, Systèmes d'Euler p-adiques et théorie d'Iwasawa, Annales de l'Institut Fourier 48 (5) (1998) 1231-1307. | Numdam | MR 1662231 | Zbl 0930.11078

[38] Schneider P, Über gewisse Galoiscohomologiegruppen, Math. Zeit. 168 (1979) 181-205. | MR 544704 | Zbl 0421.12024

[39] Schneider P, Introduction to the Beilinson conjectures, in: Beilinson's Conjectures on Special Values of L-functions, Perspectives in Math., 4, Academic Press, 1988, pp. 1-35. | MR 944989 | Zbl 0673.14007

[40] Sinnott W, On the Stickelberger ideal and the circular units of an abelian field, Invent. Math. 62 (1981) 181-234. | MR 595586 | Zbl 0465.12001

[41] Solomon D, On a construction of p-units in abelian fields, Invent. Math. 109 (1992) 329-350. | MR 1172694 | Zbl 0772.11043

[42] Soulé C, K-théorie des anneaux d'entiers de corps de nombres et cohomologie étale, Invent. Math. 55 (1979) 251-295. | MR 553999 | Zbl 0437.12008

[43] Soulé C, Régulateurs, Sém. Bourbaki (1984/85), exp. n° 644, Astérisque 133-134 (1986) 237-253. | Numdam | MR 837223 | Zbl 0617.14008

[44] Tate J, Relations between K2 and Galois cohomology, Invent. Math. 36 (1976) 257-274. | MR 429837 | Zbl 0359.12011

[45] Tsuji T, Semi-local units modulo cyclotomic units, J. Number Theory 46 (1999) 158-178. | MR 1706941 | Zbl 0948.11042

[46] Villemot L., Étude du quotient des unités semi-locales par les unités cyclotomiques dans les Zp-extensions des corps de nombres abéliens réels, thèse, Orsay, 1981. | MR 627614 | Zbl 0473.12003

[47] Washington L.C, Introduction to the Theory of Cyclotomic Fields, GTM, 85, Springer, 1982. | MR 718674