Fonctions L p -adiques

Pierre Colmez

Séminaire Bourbaki (1998-1999)

  • Volume: 41, page 21-58
  • ISSN: 0303-1179

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Colmez, Pierre. "Fonctions $L$$p$-adiques." Séminaire Bourbaki 41 (1998-1999): 21-58. <http://eudml.org/doc/110260>.

@article{Colmez1998-1999,
author = {Colmez, Pierre},
journal = {Séminaire Bourbaki},
keywords = {p-adic L-functions; Iwasawa theory; Beilinson's conjecture},
language = {fre},
pages = {21-58},
publisher = {Société Mathématique de France},
title = {Fonctions $L$$p$-adiques},
url = {http://eudml.org/doc/110260},
volume = {41},
year = {1998-1999},
}

TY - JOUR
AU - Colmez, Pierre
TI - Fonctions $L$$p$-adiques
JO - Séminaire Bourbaki
PY - 1998-1999
PB - Société Mathématique de France
VL - 41
SP - 21
EP - 58
LA - fre
KW - p-adic L-functions; Iwasawa theory; Beilinson's conjecture
UR - http://eudml.org/doc/110260
ER -

References

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  1. [1] Y. Amice, Interpolation p-adique, Bull. Soc. France92, 117-180, 1964 Zbl0158.30201MR188199
  2. [2] Y. Amice, Duals. Proc. of a conf. on p-adic analysis (Nijmegen1978), 1-15, Nijmegen, Math. Institut Katholische Univ., 1978 MR522117
  3. [3] Y. Amice et J. Vélu, Distributions p-adiques associées aux séries de Hecke, Astérisque24-25, Soc. Math. France, Paris119-131, 1975 Zbl0332.14010MR376534
  4. [4] D. Barsky, Fonctions k-lipschitziennes sur un anneau local et polynômes à valeurs entières, Bull. Soc. Math. France101, 397-411, 1973 Zbl0291.12107MR371863
  5. [5] D. Benois, On Iwasawa theory of cristalline representations, preprint 1998 
  6. [6] A. Beilinson, Higher regulators and values of L-functions, J. Soviet Math.30, 2036-2070, 1985 Zbl0588.14013MR760999
  7. [7] A. Beilinson, Polylogarithm and cyclotomic elements, preprint, 1989 
  8. [8] A. Beilinson et P. Deligne, Motivic polylogarithm and Zagier conjecture, preprint 1992 Zbl0799.19004
  9. [9] S. Bloch et K. Kato, L functions and Tamagawa numbers of motives, dans The Grothendieck Festschrift, vol. 1, Prog. in Math.86, Birkhaüser, Boston, 333-400, 1990 Zbl0768.14001MR1086888
  10. [10] F. Cherbonnier, P. Colmez, Théorie d'Iwasawa des représentations p-adiques d'un corps local, J. Amer. Math. Soc12, 241-268, 1999 Zbl0933.11056MR1626273
  11. [11] J. Coates, p-adic L functions, Séminaire Bourbaki (1988), exposé 701, Astérisque177-178, 33-59, 1989 Zbl0706.11064MR1040567
  12. [12] J. Coates et A. Wiles, On p-adic L-functions and elliptic units, J. Australian Math. Soc., A26, 1-25, 1978 Zbl0442.12007MR510581
  13. [13] R. Coleman, Division values in local fields, Inv. Math.53, 91-116, 1979 Zbl0429.12010MR560409
  14. [14] P. Colmez, Théorie d'Iwasawa des représentations de de Rham d'un corps local, Ann. Math.148, 485-571, 1998 Zbl0928.11045MR1668555
  15. [15] P. Deligne, Valeurs de fonctions L et périodes d'intégrales, dans Automorphic forms, representations and L-functions, Proc. Symp. Pure Math., American Math. Soc., 33, 313-346, 1979 Zbl0449.10022MR546622
  16. [16] J.-M. Fontaine, Sur certains types de représentations p-adiques du groupe de Galois d'un corps local; construction d'un anneau de Barsotti-Tate, Ann. Math.115, 529-577, 1982 Zbl0544.14016MR657238
  17. [17] J.-M. Fontaine, Le corps des périodes p-adiques. dans "Périodes p-adiques" exposé II, Astérisque223, 59-102, 1994 MR1293971
  18. [18] J.-M. Fontaine, Représentations p-adiques des corps locaux, dans “The Grothendieck Festschrift”, vol II, Birkhauser, Boston249-309, 1991. Zbl0743.11066
  19. [19] J.-M. Fontaine, Valeurs spéciales de fonctions L des motifs, Séminaire Bourbaki, exposé 751, Astérisque206, 205-249, 1992 Zbl0799.14006MR1206069
  20. [20] J.-M. Fontaine et B. Mazur, Geometric Galois representations, dans Elliptic curves, modular forms and Fermat's last theorem (Hong-Kong, 1993), Ser. Number Theory I, Internat. Press, Cambridge MA, 41-78, 1995 Zbl0839.14011MR1363495
  21. [21] J.-M. Fontaine et B. Perrin-Riou, Autour des conjectures de Bloch et Kato : cohomologie galoisienne et valeurs de fonctions L, dans Motives (Seattle), Proceedings of Symposia in Pure Mathematics, vol. 55, part 1, 599-706, 1994 Zbl0821.14013MR1265546
  22. [22] R. Greenberg, Iwasawa theory for p-adic representations, Adv. Stud. Pure Math.17, 97-137, 1989 Zbl0739.11045MR1097613
  23. [23] H. Hida, Elementary theory of L-functions and Eisenstein series, London Math. Soc. Stud. Texts26, Cambridge University Press, 1993 Zbl0942.11024MR1216135
  24. [24] H. Hida, On the search of genuine p-adic modular L-functions for GL(n), Mém. Soc. Math. Fr.67, 1996 Zbl0897.11015MR1479362
  25. [25] A. Huber et G. Kings, Degeneration of l-adic Eisenstein classes and of the elliptic polylog. Invent. Math.135, 545-594, 1999 Zbl0955.11027MR1669288
  26. [26] A. Huber et J. Wildeshaus, Classical motivic polylogarithm according to Beilinson and Deligne, Doc. Math.3, 27-133 et 297-299, 1998 Zbl0906.19004MR1643974
  27. [27] U. Jannsen, On the l-adic cohomology of varieties over number fields and its Galois cohomology, Galois groups over Q, Math. Sci. Res. Inst. Publ.16, 315-360, Springer, 1989 Zbl0703.14010MR1012170
  28. [28] K. Kato, Lectures on the approach to Iwasawa theory for Hasse-Weil L-functions via BdR, dans Arithmetic Algebraic Geometry, Lecture Notes in Math.1553, 1993. Zbl0815.11051MR1338860
  29. [29] K. Kato, Euler systems, Iwasawa theory and Selmer groups, preprint 1995 Zbl0993.11033MR1727298
  30. [30] K. Kato, M. Kurihara and T. Tsuji, Local Iwasawa theory of Perrin-Riou and syntomic complexes, preprint 1996 
  31. [31] V. Kolyvagin, Euler systems, The Grothendieck Festschrift, vol. 2, Prog. in Math.87, 436-483, Birkhaüser, Boston, 1990 Zbl0742.14017MR1106906
  32. [32] Y. Manin, Periods of cusp forms, and p-adic Hecke series, Math USSR-Sb.92, 371-393, 1973 Zbl0293.14008MR345909
  33. [33] B. Mazur, J. Tate et J. Teitelbaum, On p-adic analogues of the conjectures of Birch and Swinnerton-Dyer, Invent. Math.84, 1-48, 1986 Zbl0699.14028MR830037
  34. [34] B. Mazur et A. Wiles, Class fields of abelian extensions of Q, Invent. Math.76, 179-330, 1984 Zbl0545.12005MR742853
  35. [35] J. Milne, Arithmetic duality theorems, Perspectives in Mathematics, vol. 1, Academic Press, 1986. Zbl0613.14019MR881804
  36. [36] J. Nekovář, On p-adic height pairings, dans Séminaire de théorie des nombres1990-1991, édité par S. David, 127-202, BirkhaüserBoston, 1993 Zbl0859.11038MR1263527
  37. [37] J. Nekovář, Beilinson's conjectures, dans Motives (Seattle), Proceedings of Symposia in Pure Mathematics, vol. 55, part 1, 537-570, 1994 Zbl0799.19003MR1265544
  38. [38] B. Perrin-Riou, Théorie d'Iwasawa p-adique locale et globale, Invent. Math.99, 247-292, 1990 Zbl0715.11030MR1031902
  39. [39] B. Perrin-Riou, Théorie d'Iwasawa et hauteurs p-adiques, Invent. Math.109, 137-185, 1992 Zbl0781.14013MR1168369
  40. [40] B. Perrin-Riou, Théorie d'Iwasawa des représentations p-adiques sur un corps local, Invent. Math.11581-149, 1994 Zbl0838.11071MR1248080
  41. [41] B. Perrin-Riou, Fonctions L p-adiques des représentations p-adiques, Astérisque229, 1995 Zbl0845.11040MR1327803
  42. [42] B. Perrin-Riou, Fonctions L p-adiques, dans Proc. Int. Congress Math. Zürich, 400-410, Birkhäuser, 1995 Zbl0853.11093MR1403940
  43. [43] B. Perrin-Riou, Systèmes d'Euler et représentations p-adiques, Ann. Inst. Fourier48, 1231-1307, 1998 Zbl0930.11078MR1662231
  44. [44] K. Rubin, The main conjecture, Appendix to Cyclotomic fields (seconde édition) par S. Lang, Graduate Texts in Math.121, Springer-Verlag, 1990. Zbl0704.11038MR1029028
  45. [45] K. Rubin, Euler systems, Hermann Weyl lecture, livre en préparation Zbl0977.11001MR1749177
  46. [46] A. Scholl, Remarks on special values of L-functions, dans L-functions and Arithmetic, Proc. of the Durham Symp., LondonMath. Soc. L.N.S.153, Cambridge University Press, 1991, 373-392 Zbl0817.14007MR1110402
  47. [47] A. Scholl, Height pairings and special values of L-functions, dans Motives (Seattle), Proceedings of Symposia in Pure Mathematics, vol. 55, part 1, 571- 598, 1994 Zbl0817.14008MR1265545
  48. [48] A. Scholl, An introduction to Kato's Euler systems, dans Galois representations in arithmetic algebraic geometry, 379-460, Cambridge University Press, 1998 Zbl0952.11015MR1696501
  49. [49] P. Schneider, p-adic height pairings, II, Invent. Math.79, 329-374, 1985 Zbl0571.14021MR778132
  50. [50] J.-P. Serre, Sur le résidu de la fonction zêta p-adique d'un corps de nombres, C. R. Acad. Sci. Paris287 série A, 83-126, 1978 Zbl0393.12026MR506177
  51. [51] C. Soulé, Eléments cyclotomiques en K-théorie, Astérisque147-148, 225-257, 1987 Zbl0632.12014MR891430
  52. [52] J. Tate, p-divisible groups, Proc. of a conference on local fields, Nuffic Summer School at Driebergen, Springer, Berlin, 158-183, 1967 Zbl0157.27601MR231827
  53. [53] M. Vishik, Non-archimedian measures connected with Dirichlet series, Math. USSR Sbornik28, 216-228, 1976 Zbl0369.14010

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