Valeurs spéciales des fonctions L des motifs

Jean-Marc Fontaine

Séminaire Bourbaki (1991-1992)

  • Volume: 34, page 205-249
  • ISSN: 0303-1179

How to cite

top

Fontaine, Jean-Marc. "Valeurs spéciales des fonctions $L$ des motifs." Séminaire Bourbaki 34 (1991-1992): 205-249. <http://eudml.org/doc/110154>.

@article{Fontaine1991-1992,
author = {Fontaine, Jean-Marc},
journal = {Séminaire Bourbaki},
keywords = {motives; -functions; values of -series; Beilinson conjecture; Bloch-Kato conjecture},
language = {fre},
pages = {205-249},
publisher = {Société Mathématique de France},
title = {Valeurs spéciales des fonctions $L$ des motifs},
url = {http://eudml.org/doc/110154},
volume = {34},
year = {1991-1992},
}

TY - JOUR
AU - Fontaine, Jean-Marc
TI - Valeurs spéciales des fonctions $L$ des motifs
JO - Séminaire Bourbaki
PY - 1991-1992
PB - Société Mathématique de France
VL - 34
SP - 205
EP - 249
LA - fre
KW - motives; -functions; values of -series; Beilinson conjecture; Bloch-Kato conjecture
UR - http://eudml.org/doc/110154
ER -

References

top
  1. [BN78] P. Bayer et J. Neukirch. — On Values of Zeta Functions and l-adic Euler Characteristics, Invent. Math.50 (1978), 35-64. Zbl0409.12018MR516603
  2. [Be85] A. Beilinson. — Higher regulators and values of L-functions, J. Soviet. Math.30 (1985), 2036-2070. Zbl0588.14013MR760999
  3. [Be87] A. Beilinson. — Height pairing between algebraic cycles, Contemporary Math.67 (1987), 1-24. Zbl0624.14005MR902590
  4. [Be90] A. Beilinson. — Polylogarithms and cyclotomic elements, Preprint 1990. 
  5. [BGSV90] A. Beilinson, A. Goncharov, V. Schechtman and A. Varchenko. — Aomoto Dilogarithms, Mixed Hodge structures and Motivic Cohomology of Pairs of triangles on the Plane in The Grothendieck Festschrift, vol. I, Prog. in Math.86, Birkhaüser (1990), 135-172. Zbl0737.14003MR1086885
  6. [BMS87] A. Beilinson, R. Macpherson and V. Schechtman. — Notes on motivic cohomology, Duke Math. J.54 (1987), 679-710. Zbl0632.14010MR899412
  7. [BS63] B. Birch and H. Swinnerton-Dyer. — Notes on elliptic curves I, Journal de Crelle212 (1963), 7-25. Zbl0118.27601MR146143
  8. [BS65] B. Birch and H. Swinnerton-Dyer. — Notes on elliptic curves II, Journal de Crelle218 (1965), 79-108. Zbl0147.02506MR179168
  9. [B180] S. Bloch. — A note on height pairings, Tamagawa numbers and Swinnerton-Dyer conjecture, Invent. Math.58 (1980), 65-76. Zbl0444.14015MR570874
  10. [B184] S. Bloch. — Algebraic cycles and values of L-functions, Journal de Crelle350 (1984), 94-108. Zbl0527.14008MR743535
  11. [B184b] S. Bloch. — Height pairings for algebraic cycles, Journal of Pure and Applied Algebra34 (1984), 119-145. Zbl0577.14004MR772054
  12. [B186] S. Bloch. — Algebraic cycles and the Beilinson conjectures, Contemporary Math.58 (1986), 65-79. Zbl0605.14017MR860404
  13. [BK90] S. Bloch et K. Kato. — L functions and Tamagawa numbers of motives, in The Grothendieck Festschrift, vol. 1, Prog. in Math.86, Birkhaüser, Boston (1990), 333-400. Zbl0768.14001MR1086888
  14. [CL88] L. Clozel. — Nombres de Tamagawa des groupes semi-simples (d'après Kottwitz), Séminaire Bourbaki, exp. 702, novembre 1988. Zbl0705.11028
  15. [Co89] J. Coates. — On p-adic L-functions, Séminaire Bourbaki, exp. 701, novembre 1988. Zbl0706.11064MR1040567
  16. [Co91] J. Coates. — Motivic p-adic L-functions, in L-functions and Arithmetic, Proc. of the Durham Symposium, London Math. Soc. L.N.S.153, Cambridge University Press (1991), 141-172. Zbl0725.11029MR1110392
  17. [CP89] J. Coates and B. Perrin-Riou. — On p-adic L-functions attached to motives over Q, Adv. Stud. Pure Math.17, (1989), 23-54. Zbl0783.11039MR1097608
  18. [De71] P. Deligne. — Théorie de Hodge II, Pub. Math. I.H.E.S.40 (1971), 5-57. Zbl0219.14007MR498551
  19. [De73] P. Deligne. — Les constantes des équations fonctionnelles des fonctions L in Modular Functions of One Variable, vol. 2, Lecture Notes in Math. 349, Springer1973, 501-595. Zbl0271.14011MR349635
  20. [De74] P. Deligne. — Théorie de Hodge III, Pub. Math. I.H.E.S.44 (1974), 5-77. Zbl0237.14003MR498552
  21. [De79] P. Deligne. — Valeurs de fonctions L et périodes d'intégrales, AMS, Proc. Symp. Pure Math.33 (1979), 313-346. Zbl0449.10022MR546622
  22. [De83] P. Deligne. — Preuve des Conjectures de Tate et de Shafarevitch (d'après G. Faltings), Séminaire Bourbaki, exp. 616, novembre 1983. Zbl0591.14026
  23. [De85] P. Deligne. — Lettre à C. Soulé, 1985. 
  24. [De89] P. Deligne. — Le groupe fondamental de la droite projective moins trois points in Galois Groups over Q, MSRI publications16, Springer1989, 79-297. Zbl0742.14022MR1012168
  25. [DM82] P. Deligne and J. Milne. — Tannakian categories in Hodge Cycles, Motives and Shimura Varieties, Lecture Notes in Math.900, Springer1982, 101-228. Zbl0477.14004MR654325
  26. [Den91] C. Deninger. — On the Γ-factors attached to motives, Invent. Math.104 (1991), 245-261. Zbl0739.14010
  27. [Den92] C. Deninger. — Local L-factors of motives and regularized determinants, Invent. Math.107 (1992), 137-150. Zbl0762.14015MR1135468
  28. [DS91] C. Deninger and A. Scholl. — The Beilinson conjectures, in L- functions and Arithmetic, Proc. of the Durham Symposium, London Math. Soc. L.N.S.153, Cambridge University Press (1991), 173-209. Zbl0729.14002MR1110393
  29. [Fa89] G. Faltings. — Crystalline cohomology and p-adic Galois representations, in Algebraic analysis, geometry and number theory, Johns Hopkins University Press, Baltimore (1989), 25-80. Zbl0805.14008MR1463696
  30. [Fa90] G. Faltings. — F-isocrystals on Open Varieties : Results and Conjectures, in The Grothendieck Festschrift, vol. 2, Prog. in Math.87, Birkhaüser, Boston (1990), 219-248. Zbl0736.14004MR1106900
  31. [FI90] J.-M. Fontaine et L. Illusie. — p-adic periods : a survey, prépu- blication d'Orsay, 1990. 
  32. [FM92] J.-M. Fontaine et B. Mazur. — Représentations l-adiques géométriques, in [Bures], en préparation. 
  33. [FP91] J.-M. Fontaine et B. Perrin-Riou. — Autour des conjectures de Bloch et Kato : I : Cohomologie galoisienne, II : Structures motiviques f-closes, III : Le cas général, C.R. Acad. Sci. Paris, 313, série I, 1991, 189-196, 349-356 et 421-428. Zbl0752.14001MR1126377
  34. [FP92] J.-M. Fontaine et B. Perrin-Riou. — Autour des conjectures de Bloch et Kato : cohomologie galoisienne et valeurs de fonctions L, prépublication d'Orsay, 1992. 
  35. [Gr90] M. Gros. — Régulateurs syntomiques et valeurs de fonctions L p-adiques (avec un appendice de M. Kurihara : Computation of the syntomic regulator in the cyclotomic case), Invent. Math.99 (1990), 293-320. Zbl0667.14006MR1031903
  36. [Gr91] B. Gross. — Kolyvagin's work for modular elliptic curves, in L— functions and Arithmetic, London Math. Soc. L. Note Ser. vol. 153, Cambridge Univ. Press1991, 235-256. Zbl0743.14021MR1110395
  37. [Gre89] R. Greenberg. — Iwasawa theory for p-adic representations, Adv. Stud. Pure Math.17, (1989), 97-137. Zbl0739.11045MR1097613
  38. [Gre91] R. Greenberg. — Iwasawa theory for motives, in L-functions and Arithmetic, Proc. of the Durham Symposium, London Math. Soc. L.N.S.153, Cambridge University Press (1991), 373-392. Zbl0727.11043MR1110394
  39. [Ha89] G. Harder. — Arithmetische Eigenschaften von Eisenstein Klassen. die modulare Konstruktion von gemischten Motiven und von Erweiterungen endlicher Galoismoduln, Preprint 1989. 
  40. [I190] L. Illusie. — Cohomologie de de Rham et cohomologie étale p-adique, Séminaire Bourbaki, exp. 726, juin 1990. 
  41. [Ja88] U. Jannsen. — Deligne Homology, Hodge-D-conjecture, and Motives, in [RSS88], 305-372. Zbl0701.14019MR944998
  42. [Ja89] U. Jannsen. — On the l-adic cohomology of varieties over number fields and its Galois cohomology, in Galois groups over Q, MSRI Publications vol. 16, Springer1989. Zbl0703.14010MR1012170
  43. [Ja90] U. Jannsen. — Mixed motives and algebraic K-theory, Lecture Notes in Math.1400, Springer, Berlin (1990). Zbl0691.14001MR1043451
  44. [Ka91] K. Kato. — Iwasawa theory and p-adic Hodge theory, preprint 1991. MR1207986
  45. [Ko90] V.A. Kolyvagin. — Euler Systems, in the Grothendieck Festschrift, vol. II, Prog. in Math.87, Birkhäuser (1990), 435-483. Zbl0742.14017MR1106906
  46. [Li72] S. Lichtenbaum. — On the values of zeta and L-functions : I, Annals of Math.96 (1972), 338-360. Zbl0251.12002MR360527
  47. [Li84] S. Lichtenbaum. — Values of zeta functions at non-negative integers in Number Theory, Noordwijkerhout, Lecture Notes in Math.1068, Springer, Berlin (1984), 127-138. Zbl0591.14014MR756089
  48. [Li87] S. Lichtenbaum. — The Construction of Weight-two Arithmetic Cohomolgy, Invent. Math.88 (1987), 183-215. Zbl0615.14004MR877012
  49. [Mi86] J.S. Milne. — Arithmetic duality theorems, Perspectives in Mathematics, vol. 1, Academic Press (1986). Zbl0613.14019MR881804
  50. [MW84] B. Mazur and A. Wiles. — Class fields of abelian extensions of Q, Invent. Math.76 (1984), 179-330. Zbl0545.12005MR742853
  51. [Ne92] J. Nekovar. — Kolyvagin's method for Chow groups of Kuga-Sato varieties, Invent. Math.107 (1992), 99-125. Zbl0729.14004MR1135466
  52. [Ne92b] J. Nekovar. — On p-adic height pairing, Séminaire de Théorie des Nombres de Paris, à paraître. Zbl0859.11038
  53. [Pa91] A. Panchishkin. — Non Archimedian L-Functions of Siegel and Hilbert Modular Forms, Lecture Notes in Math.1471, Springer1991. Zbl0732.11026MR1122593
  54. [Pe89] B. Perrin-Riou. — Travaux de Kolyvagin et Rubin, Séminaire Bourbaki, exp. 717, novembre 1989. Zbl0735.14017MR1099872
  55. [Pe92] B. Perrin-Riou. — Théorie d'Iwasawa et hauteur p-adique, Invent. Math.109 (1992), 137-185. Zbl0781.14013MR1168369
  56. [Ra89] D. Ramakrishnan. — Regulators, Algebraic Cycles, and Values of L-Functions, in Algebraic K-theory and Algebraic Number Theory, Contemporary Mathematics, vol. 83, Amer. Math. Soc., Providence (1989), 183-310. Zbl0694.14002MR991982
  57. [Ra90] D. Ramakrishnan. — Problems arising from the Tate and Beilinson Conjectures in the context of Shimura Varieties, in Automorphic Forms, Shimura Varieties, and L-functions, vol. II, Perspectives in Mathematics, vol. 11, Academic Press (1990), 227-252. Zbl0714.14022MR1044831
  58. [RSS88] M. Rapoport, N. Schappacher and P. Schneider (éd.). — Beilin- son's Conjectures on Special Values of L-Functions, Perspectives in Mathematics, vol. 4, Academic Press, Boston (1988). Zbl0635.00005MR944987
  59. [Ru91] K. Rubin. — The "main conjectures" of Iwasawa theory for imaginary quadratic fields, Invent. Math.103 (1991), 25-68. Zbl0737.11030MR1079839
  60. [Sc88] P. Schneider. — Introduction to the Beilinson conjectures, in [RSS88], 1-35. Zbl0673.14007MR944989
  61. [Sc89] P. Schneider. — Motivic Iwasawa theory, Adv. Stud. Pure Math.17, (1989), 421-456. Zbl0741.11042MR1097626
  62. [Sc90] A.J. Scholl. — Motives for modular forms, Invent. Math.100 (1990), 419-430. Zbl0760.14002MR1047142
  63. [Sc91] A.J. Scholl. — Remarks on special values of L-functions, in L- functions and Arithmetic, Proc. of the Durham Symposium, London Math. Soc. L.N.S.153, Cambridge University Press (1991), 373-392. Zbl0817.14007MR1110402
  64. [Se70] J.-P. Serre. — Facteurs locaux des fonctions zêta des variétés algébriques (définitions et conjectures), in Collected Papers, vol. 2, SpringerBerlin (1986), 581-592. 
  65. [ST68] J.-P. Serre and J.-P. Tate. — Good reduction of abelian varieties, Ann. of Math.88 (1968), 492-517. Zbl0172.46101MR236190
  66. [So79] C. Soulé. — K-théorie des anneaux d'entiers de corps de nombres et cohomologie étale, Invent. Math.55 (1979), 251-295. Zbl0437.12008MR553999
  67. [So81] C. Soulé. — On higher p-adic regulators, in Algebraic K-theory, Lecture Notes in Math.854, Springer, Berlin (1981), 371-401. Zbl0488.12008MR618313
  68. [So83] C. Soulé. — K-théorie et zéros aux points entiers de fonctions zéta, Proc. ICM.Warszawa (1983). Zbl0574.14010MR804699
  69. [So85] C. Soulé. — Régulateurs, Séminaire Bourbaki, exp. 644, février 1985. Zbl0617.14008MR837223
  70. [So87] C. Soulé. — p-adic K-theory of elliptic curves, Duke Math. Journal54 (1987), 249-269. Zbl0627.14010MR885785
  71. [Ta65] J. Tate. — Algebraic cycles and poles of zeta functions, in Arithmetical Algebraic Geometry, Harper and Row, New York (1965). Zbl0213.22804MR225778
  72. [Ta66] J. Tate. — On the Conjectures of Birch and Swinnerton-Dyer and a geometric analog, Séminaire Bourbaki, exp. 306, février 1966. Zbl0199.55604
  73. [Ta79] J. Tate. — Number theoretic Background, in Proceedings of Symposia in Pure Mathematics, vol. 33 (1979), part 2, 3-26. Zbl0422.12007MR546607
  74. [Ta84] J. Tate. — Les Conjectures de Stark sur les Fonctions L d'Artin en s = 0, Birkhaüser, Boston (1984). Zbl0545.12009MR782485
  75. [Bures] Séminaire sur les périodes p-adiques (tenu à Bures en 1988), actes en prépartion. 
  76. [SGA4] Théorie des topos et cohomologie étale des schémas, dirigé par M. Artin, A. Grothendieck et J.-L. Verdier, Lecture Notes in Math.269, 270 et 305, Springer, Berlin (1972-73). MR354653
  77. [SGA 1/2] Cohomologie étale, par P. Deligne, Lecture Notes in Math. 569, Springer, Berlin (1977). Zbl0345.00010MR463174
  78. [SGA5] Cohomologie l-adique et Fonctions L, dirigé par A. Grothendieck, Lecture Note in Math.589, Springer, Berlin (1977). MR491704

Citations in EuDML Documents

top
  1. Arthur Jaffe, Frank Quinn, „Teoretická matematika‟ aneb Jak smířit matematiku s teoretickou fyzikou
  2. Rob de Jeu, Tejaswi Navilarekallu, [unknown]
  3. Jean-Michel Kantor, Les problèmes de Hilbert et leur devenir
  4. Guido Kings, The Bloch-Kato conjecture on special values of L -functions. A survey of known results
  5. Pierre Colmez, Fonctions L p -adiques
  6. Denis Benois, Thong Nguyen Quang Do, Les nombres de Tamagawa locaux et la conjecture de Bloch et Kato pour les motifs Q(m) sur un corps abélien
  7. Fred Diamond, Matthias Flach, Li Guo, The Tamagawa number conjecture of adjoint motives of modular forms

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.