Homologie du groupe linéaire et polylogarithmes

Jean-Louis Cathelineau

Séminaire Bourbaki (1992-1993)

  • Volume: 35, page 311-341
  • ISSN: 0303-1179

How to cite

top

Cathelineau, Jean-Louis. "Homologie du groupe linéaire et polylogarithmes." Séminaire Bourbaki 35 (1992-1993): 311-341. <http://eudml.org/doc/110173>.

@article{Cathelineau1992-1993,
author = {Cathelineau, Jean-Louis},
journal = {Séminaire Bourbaki},
keywords = {Wigner-Bloch -logarithm; polylogarithm; rank conjecture; Zagier conjecture; antisymmetric symbol; trilogarithm; regulators},
language = {fre},
pages = {311-341},
publisher = {Société Mathématique de France},
title = {Homologie du groupe linéaire et polylogarithmes},
url = {http://eudml.org/doc/110173},
volume = {35},
year = {1992-1993},
}

TY - JOUR
AU - Cathelineau, Jean-Louis
TI - Homologie du groupe linéaire et polylogarithmes
JO - Séminaire Bourbaki
PY - 1992-1993
PB - Société Mathématique de France
VL - 35
SP - 311
EP - 341
LA - fre
KW - Wigner-Bloch -logarithm; polylogarithm; rank conjecture; Zagier conjecture; antisymmetric symbol; trilogarithm; regulators
UR - http://eudml.org/doc/110173
ER -

References

top
  1. [1] A.A. Beilinson, Higher regulators and values of L-functions, Sovr. Probl. Math., 24 (1984), 181-238. Zbl0588.14013MR760999
  2. [2] A.A. Beilinson, Polylogarithms and cyclotomic elements, preprint. 
  3. [3] A.A. Beilinson, P. Deligne, Motivic polylogarithms and Zagier conjecture, preprint. Zbl0799.19004
  4. [4] A.A. Beilinson, A.B. Goncharov, V.V. Schechtman, A.N. Varchenko, Projective geometry and algebraic K-theory, Leningrad math. Jo.2 (1991), 523-576. Zbl0728.14008MR1073210
  5. [5] A.A. Beilinson, R. MacPherson, V.V. Schechtman, Notes on motivic cohomology, Duke Math. J., 54 (1987), 679-710. Zbl0632.14010MR899412
  6. [6] S. Bloch, Higher regulators, algebraic K-theory and zeta functions of elliptic curves, Lect. notes, Irvine, 1977. 
  7. [7] S. Bloch, Applications of the dilogarithm function in algebraic K-theory and algebraic geometry, Proc. Int. Symp. Alg. Geom., Kyoto (1977) 1- 14. Zbl0416.18016MR578856
  8. [8] S. Bloch, Algebraic cycles and algebraic K-theory, Adv. in Math., 6 (1986), 267-304. Zbl0608.14004MR852815
  9. [9] A. Borel, Cohomologie de SL2 et valeurs de fonctions zêta aux points entiers, Ann. Ec. Norm. Sup. Pisa, 4 (1974), 613-636. Zbl0382.57027MR506168
  10. [10] A. Borel, Stable real cohomology of arithmetic groups, Ann. Sci. Ec. Norm. Sup., 7 (1974), 235-274. Zbl0316.57026MR387496
  11. [11] H. Cartan, La transgression dans un groupe de Lie et dans un espace fibré principal, Colloque de topologie, Liège (1950), 57-71. Zbl0045.30701MR42427
  12. [12] P. Cartier, Décomposition des polyèdres, le point sur le troisième problème de Hilbert, Sém. Bourbaki1984/85, exp. 646, Astérique133/134 (1986), 261-288. Zbl0589.51032MR837225
  13. [13] J.L. Cathelineau, Birapport et groupoïdes, preprint. MR1365847
  14. [14] P. Deligne, Théorie de Hodge III, Publ. Math. IHES, 44 (1974), 5-27. Zbl0237.14003MR498552
  15. [15] P. Deligne, Interprétation motivique de la conjecture de Zagier reliant polylogarithmes et régulateurs, preprint 1990. MR296076
  16. [16] J. Dupont, The dilogarithm as a characteristic class for flat bundles, J. of Pure and Appl. Alg., 44 (1987), 137-164. Zbl0624.57024MR885101
  17. [17] J. Dupont, Characteristic classes for flat bundles and their formulas, preprint, Aarhus1993. MR1286932
  18. [18] J. Dupont, R. Hain, S. Zucker, Regulators and characteristic classes of flat bundles, preprint Aarhus1992. Zbl0976.14005MR1736876
  19. [19] J. Dupont, C.H. Sah, Scissors congruences II, Jo. Pure Appl. Alg., 25 (1982), 159-195. Zbl0496.52004MR662760
  20. [20] H. Esnault, E. Viehweg, Deligne-Beilinson cohomology, in Beilinson's conjectures on special values of L-functions, 43-81, Perspectives in Math.1988, Acad. Press. Zbl0656.14012MR944991
  21. [21] A. Gabrielov, I.M. Gelfand, M.H. Losik, Combinatorial calculation of characteristic classes, Funct. Anal. i Priloz.9 (1975), (1) 54-55, (2) 12-28, (3) 5-26. Zbl0312.57015MR410758
  22. [22] I.M. Gelfand, R. MacPherson, Geometry in grassmannians and a generalization of the dilogarithm, Adv. in Math.44 (1982), 279-312. Zbl0504.57021MR658730
  23. [23] W. Gerdes, Affine grassmannian homology and the homology of the general linear groups, Duke Math. J., (1) 62 (1991), 85-103. Zbl0743.14007MR1104324
  24. [24] W. Gerdes, The linearization of higher Chow cycles of dimension one, Duke Math. J., (1) 62 (1991), 105-109. Zbl0754.14005MR1104325
  25. [25] A.B. Goncharov, The classical polylogarithm, algebraic K-theory of fields and Dedekind zeta functions, Bull. A. M. S., (1) 29 (1991), 155- 161. Zbl0731.19006MR1056557
  26. [26] A.B. Goncharov, Geometry of configurations, polylogarithms and motivic cohomology, preprint Max Planck Inst.1992. MR1348706
  27. [27] A.B. Goncharov, Polylogarithms and motivic Galois groups, Proc. of the Seattle conf. on motives, Seattle july 1991, preprint. Zbl0842.11043MR1265551
  28. [28] A.B. Goncharov, Explicit construction of characteristic classes, preprint Max Planck Inst.1992. MR1237830
  29. [29] S. Govindachar, Explicit weight two motivic cohomology complexes and algebraic K-theory, K-theory, 6 (1992), 387-430. Zbl0782.14005MR1194842
  30. [30] R. Hain, Classical polylogarithms, preprint. MR1265550
  31. [31] R. Hain, R. MacPherson, Higher logarithms, Illinois J. of Math., 34 (1990), 392-475. Zbl0737.14014MR1046570
  32. [32] M. Hanamura, R. MacPherson, Geometric construction of polylogarithms, Duke Math. J., 70 (1993) 481-515. Zbl0824.14043MR1224097
  33. [33] H. Hiller, λ-ring and algebraic K-theory, J. of Pure and Appl. Alg., 20 (1981), 241-266. Zbl0471.18007
  34. [34] W. Hulshergen, Conjectures in arithmetic algebraic geometry, a survey, Aspects of Math., Vieweg1992. Zbl0745.14006MR1150049
  35. [35] K. Igusa, The Borel regulator map on pictures, preprint. Zbl0793.19001
  36. [36] M. Karoubi, Classes caractéristiques de fibrés feuilletés, holomorphes ou algébriques, preprint Univ. Paris VII, 52 (1993). Zbl0833.57012MR1273841
  37. [37] C. Kratzer, λ-structure en K-théorie algébrique, Comm. Math. Helv., 55 (1980), 233-254. Zbl0444.18008
  38. [38] S. Lichtenbaum, The construction of weight two arithmetic cohomology, Inv. Math., 88 (1987), 183-215. Zbl0615.14004MR877012
  39. [39] J.L. Loday, K-théorie algébrique et représentations de groupes, Ann. Sci. Ec. Norm. Sup., (4) 9 (1976), 309-377. Zbl0362.18014MR447373
  40. [40] J.L. Loday, Symboles en K-théorie algébrique d'ordre supérieur, Comptes rendus Acad. Sci. Paris, 292 (1981), 863-866. Zbl0493.18006MR623517
  41. [41] J. Milnor, Algebraic K-theory and quadratic forms, Inv. Math., 9 (1970), 318-344. Zbl0199.55501MR260844
  42. [42] J. Milnor, J. Moore, On the structure of Hopf algebras, Ann. of Math., (2) 81 (1965), 211-264. Zbl0163.28202MR174052
  43. [43] D. Mumford, Projective invariants of projective structures and applications, Proc. Int. Cong. of Math.1962, Stockholm, 526-530. Zbl0154.20702MR175899
  44. [44] J. Oesterlé, Polylogarithmes, Sém. Bourbaki, 762 (1992-93). Zbl0799.11056MR1246392
  45. [45] D. Quillen, Higher algebraic K-theory I, Springer Lect. Notes in Math., 341 (1973), 85-197. Zbl0292.18004MR338129
  46. [46] D. Ramakrishnan, Regulators, algebraic cycles and values of L-functions, Contemp. Math., 83 (1989), 183-310. Zbl0694.14002MR991982
  47. [47] M. Rapoport, Comparison of the regulator of Beilinson and of Borel, in Beilinson's conjectures on special values of L-functions, 169-192, Perspectives in Math.1988, Acad. Press. Zbl0667.14005MR944994
  48. [48] P. Schneider, Introduction to the Beilinson Conjectures, in Beilinson's conjectures on special values of L-functions, 1-35, Perspectives in Math.1988, Acad. Press. Zbl0673.14007MR944989
  49. [49] Ch. Soulé, Opérations en K-théorie algébrique, Canad. J. of Math., 27 (1985), 488-550. Zbl0575.14015MR787114
  50. [50] Ch. Soulé, Régulateurs, Sém. Bourbaki1984/85, exp. 644, Astérique133/134 (1986), 237-253. Zbl0617.14008MR837223
  51. [51] A.A. Suslin, Homology of GLn, characteristic classes and Milnor K-theory, Springer Lect. Notes in Math., 1046 (1989), 357-375. Zbl0528.18007MR750690
  52. [52] A.A. Suslin, Algebraic K-theory of fields, Proc. Int. Cong. of Math.1986, Berkeley, 222-243. Zbl0675.12005MR934225
  53. [53] A.A. Suslin, K3 of a field and the Bloch group, Proc. Steklov inst. of Math., 4 (1991), 217-239. Zbl0741.19005MR1124626
  54. [54] J. Tate, Symbols in Arithmetic, Actes Cong. Int. Nice, 1970, tome 1, 201-211, Gauthier-Villars1971. Zbl0229.12013MR422212
  55. [55] B. Totaro, Milnor K-theory is the simplest part of algebraic K-theory, K-theory, 6 (1992), 177-189. Zbl0776.19003MR1187705
  56. [56] W.T. VanEst, Group cohomology and Lie algebra cohomology in Lie groups, Indag. Math., 15 (1953), 484-504. Zbl0051.26001
  57. [57] J. Yang, On the real cohomology of arithmetic groups and the rank conjecture for number fields, Ann. Ecole Norm. Sup., 25 (1992), 287- 306. Zbl0770.11028MR1169133
  58. [58] J. Yang, The Hain-MacPherson third logarithm, the third Borel regulator and the values of Dedekind zeta function at 3, preprint. 
  59. [59] D. Zagier, Hyperbolic manifolds and special values of Dedekind zeta functions, Inv. Math., 83 (1986), 285-301. Zbl0591.12014MR818354
  60. [60] D. Zagier, Polylogarithms, Dedekind zeta functions and the algebraic K-theory of fields, Proc. Texel Conf. on Arithm. Alg. Geometry1989, Birkhäuser, Boston (1991), 391-430. Zbl0728.11062MR1085270

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.