Les nombres de Tamagawa locaux et la conjecture de Bloch et Kato pour les motifs Q(m) sur un corps abélien

 Access to full text

 Full (PDF)

1. [1] Banaszak G, Generalization of the Moore exact sequence and the wild kernel for higher K-groups, Compositio Math.86 (3) (1993) 281-305. Zbl0778.11066MR1219629
2. [2] Beilinson A., Polylogarithms and cyclotomic elements, Preprint, 1990. 
3. [3] Belliard J.-R, Nguyen Quang Do T, Formules de classes pour les corps abéliens réels, Ann. Inst. Fourier51 (4) (2001) 903-937. Zbl1007.11063MR1849210
4. [4] Belliard J.-R., Nguyen Quang Do T., Modified circular p-units and annihilation of real classes, prépublication, 2001. 
5. [5] Benois D., Burns D., travail en préparation. 
6. [6] Borel A, Cohomologie de SLn et valeurs de fonctions zêta, Ann. Scuola Norm. Sup. Pisa417 (1974) 613-636. Zbl0382.57027MR506168
7. [7] Bloch S, Kato K, L-functions and Tamagawa numbers of motives, Grothendieck Festschrift1 (1990) 333-400. Zbl0768.14001MR1086888
8. [8] Burns D, Flach M, Motivic L-functions and Galois module structure, Math. Ann.305 (1996) 65-102. Zbl0867.11081MR1386106
9. [9] Burns D., Greither C., On the equivariant Tamagawa number conjecture for Tate motives, Preprint, 2000. Zbl1142.11076MR1992015
10. [10] Beilinson A, MacPherson R, Schechtman V, Notes on motivic cohomology, Duke Math. J.54 (1987) 679-710. Zbl0632.14010MR899412
11. [11] Coleman R, Local units modulo circular units, Proc. Amer. Math. Soc.89 (1983) 1-7. Zbl0528.12005MR706497
12. [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. Zbl0742.14022MR1012168
13. [13] Dwyer W.-G, Friedlander E.M, Algebraic and etale K-theory, Trans. Amer. Math. Soc.292 (1985) 247-280. Zbl0581.14012MR805962
14. [14] Flach M, A generalization of the Cassels–Tate pairing, J. Reine Angew. Math.412 (1990) 113-127. Zbl0711.14001MR1079004
15. [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. Zbl0544.14016MR657238
16. [16] Fontaine J.-M, Le corps des périodes p-adiques, Astérisque223 (1994) 59-102. MR1293971
17. [17] Fontaine J.-M, Valeurs spéciales de fonctions L des motifs, Séminaire Bourbaki, exposé 751, Astérisque206 (1992) 205-249. Zbl0799.14006MR1206069
18. [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. Zbl0821.14013MR1265546
19. [19] Gillard R, Unité cyclotomiques, unités semi-locales et Zl-extensions, Ann. Inst. Fourier29 (1) (1979) 49-79. Zbl0387.12002MR526777
20. [20] Greither C, Class groups of abelian fields and the main conjecture, Ann. Inst. Fourier42 (1992) 449-499. Zbl0729.11053MR1182638
21. [21] Gross B.H., On the values of Artin L-functions, Preprint, 1980. MR2154331
22. [22] Huber A., Kings G., Bloch–Kato conjecture and main conjecture of Iwasawa theory for Dirichlet characters, Preprint, 2000. MR2002643
23. [23] Huber A, Wildeshaus J, Classical motivic polylogarithm according to Beilinson and Deligne, Doc. Math. J.DMV3 (1998) 27-133. Zbl0906.19004MR1643974
24. [24] Kahn B, On the Lichtenbaum–Quillen conjecture, in: Algebraic K-theory and Algebraic Topology, NATO Proc. Lake Louise, 407, 1993, pp. 147-166. Zbl0885.19004MR1367295
25. [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. Zbl0815.11051MR1338860
26. [26] Kato K., Lectures on the approach to Iwasawa theory for Hasse–Weil L-functions via BdR. Part II, Preprint, 1993. Zbl0815.11051MR1338860
27. [27] Kolster M., Nguyen Quang Do T., Universal distribution lattices for abelian number fields, Preprint, 2000. 
28. [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. Zbl0863.19003MR1408541
29. [29] Kuzmin L.V, On formulae for the class number of real abelian fields, Russian Math. Izv.60 (4) (1996) 695-761. Zbl1007.11065MR1416925
30. [30] Leopoldt H.-W, Über die Hauptordnung der ganzen Elemente eines abelschen Zahlkörpers, J. Reine Angew. Math.201 (1959) 119-149. Zbl0098.03403MR108479
31. [31] Lettl G, Relative Galois module structure of integers of local abelian fields, Acta Arithmetica85 (3) (1998) 235-247. Zbl0910.11050MR1627831
32. [32] Milne J.S, Arithmetic Duality Theorems, Perspectives in Mathematics, 1, Academic Press, Boston, 1986. Zbl0613.14019MR881804
33. [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. Zbl0651.12009MR944995
34. [34] Nguyen Quang Do T, Analogues supérieurs du noyau sauvage, J. Théorie des Nombres Bordeaux4 (1992) 263-271. Zbl0783.11042MR1208865
35. [35] Perrin-Riou B, Théorie d'Iwasawa des représentations p-adiques sur un corps local, Invent. Math.115 (1994) 81-149. Zbl0838.11071MR1248080
36. [36] Perrin-Riou B, Fonctions Lp-adiques, in: Proc. Int. Congress of Math., Birkhäuser Verlag, Zürich, 1995, pp. 400-410. Zbl0853.11093MR1403940
37. [37] Perrin-Riou B, Systèmes d'Euler p-adiques et théorie d'Iwasawa, Annales de l'Institut Fourier48 (5) (1998) 1231-1307. Zbl0930.11078MR1662231
38. [38] Schneider P, Über gewisse Galoiscohomologiegruppen, Math. Zeit.168 (1979) 181-205. Zbl0421.12024MR544704
39. [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. Zbl0673.14007MR944989
40. [40] Sinnott W, On the Stickelberger ideal and the circular units of an abelian field, Invent. Math.62 (1981) 181-234. Zbl0465.12001MR595586
41. [41] Solomon D, On a construction of p-units in abelian fields, Invent. Math.109 (1992) 329-350. Zbl0772.11043MR1172694
42. [42] Soulé C, K-théorie des anneaux d'entiers de corps de nombres et cohomologie étale, Invent. Math.55 (1979) 251-295. Zbl0437.12008MR553999
43. [43] Soulé C, Régulateurs, Sém. Bourbaki (1984/85), exp. n° 644, Astérisque133–134 (1986) 237-253. Zbl0617.14008MR837223
44. [44] Tate J, Relations between K2 and Galois cohomology, Invent. Math.36 (1976) 257-274. Zbl0359.12011MR429837
45. [45] Tsuji T, Semi-local units modulo cyclotomic units, J. Number Theory46 (1999) 158-178. Zbl0948.11042MR1706941
46. [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. Zbl0473.12003MR627614
47. [47] Washington L.C, Introduction to the Theory of Cyclotomic Fields, GTM, 85, Springer, 1982. MR718674

1. Guido Kings, The Bloch-Kato conjecture on special values of $L$-functions. A survey of known results
2. Thong Nguyen Quang Do, Conjecture principale équivariante, idéaux de Fitting et annulateurs en théorie d’Iwasawa