Homologie du groupe linéaire et polylogarithmes [d'après A.B. Goncharov et d'autres]

Cathelineau, Jean-Louis

Séminaire Bourbaki : volume 1992/93, exposés 760-774, Astérisque, no. 216 (1993), Exposé no. 772, 31 p.

@incollection{SB_1992-1993__35__311_0,
     author = {Cathelineau, Jean-Louis},
     title = {Homologie du groupe lin\'eaire et polylogarithmes [d'apr\`es {A.B.} {Goncharov} et d'autres]},
     booktitle = {S\'eminaire Bourbaki : volume 1992/93, expos\'es 760-774},
     series = {Ast\'erisque},
     note = {talk:772},
     pages = {311--341},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {216},
     year = {1993},
     mrnumber = {1246402},
     zbl = {0845.19003},
     language = {fr},
     url = {https://www.numdam.org/item/SB_1992-1993__35__311_0/}
}

TY  - CHAP
AU  - Cathelineau, Jean-Louis
TI  - Homologie du groupe linéaire et polylogarithmes [d'après A.B. Goncharov et d'autres]
BT  - Séminaire Bourbaki : volume 1992/93, exposés 760-774
AU  - Collectif
T3  - Astérisque
N1  - talk:772
PY  - 1993
SP  - 311
EP  - 341
IS  - 216
PB  - Société mathématique de France
UR  - https://www.numdam.org/item/SB_1992-1993__35__311_0/
LA  - fr
ID  - SB_1992-1993__35__311_0
ER  -

%0 Book Section
%A Cathelineau, Jean-Louis
%T Homologie du groupe linéaire et polylogarithmes [d'après A.B. Goncharov et d'autres]
%B Séminaire Bourbaki : volume 1992/93, exposés 760-774
%A Collectif
%S Astérisque
%Z talk:772
%D 1993
%P 311-341
%N 216
%I Société mathématique de France
%U https://www.numdam.org/item/SB_1992-1993__35__311_0/
%G fr
%F SB_1992-1993__35__311_0

Cathelineau, Jean-Louis. Homologie du groupe linéaire et polylogarithmes [d'après A.B. Goncharov et d'autres], dans Séminaire Bourbaki : volume 1992/93, exposés 760-774, Astérisque, no. 216 (1993), Exposé no. 772, 31 p. https://www.numdam.org/item/SB_1992-1993__35__311_0/

Bibliographie
Cité par

[1] A. A. Beilinson, Higher regulators and values of $L$ -functions, Sovr. Probl. Math., 24 (1984), 181-238. | MR | Zbl

[2] A. A. Beilinson, Polylogarithms and cyclotomic elements, preprint.

[3] A. A. Beilinson, P. Deligne, Motivic polylogarithms and Zagier conjecture, preprint.

[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. | MR | Zbl

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

[6] S. Bloch, Higher regulators, algebraic $K$ -theory and zeta functions of elliptic curves, Lect. notes, Irvine, 1977.

[7] S. Bloch, Applications of the dilogarithm function in algebraic $K$ -theory and algebraic geometry, Proc. Int. Symp. Alg. Geom., Kyoto (1977) 1- 14. | MR | Zbl

[8] S. Bloch, Algebraic cycles and algebraic $K$ -theory, Adv. in Math., 6 (1986), 267-304. | MR | Zbl

[9] A. Borel, Cohomologie de $S L_{2}$ et valeurs de fonctions zêta aux points entiers, Ann. Ec. Norm. Sup. Pisa, 4 (1974), 613-636. | Numdam | MR | Zbl

[10] A. Borel, Stable real cohomology of arithmetic groups, Ann. Sci. Ec. Norm. Sup., 7 (1974), 235-274. | Numdam | MR | Zbl

[11] H. Cartan, La transgression dans un groupe de Lie et dans un espace fibré principal, Colloque de topologie, Liège (1950), 57-71. | MR | Zbl

[12] P. Cartier, Décomposition des polyèdres, le point sur le troisième problème de Hilbert, Sém. Bourbaki 1984/85, exp. 646, Astérique 133/134 (1986), 261-288. | Numdam | MR | Zbl

[13] J. L. Cathelineau, Birapport et groupoïdes, preprint. | MR

[14] P. Deligne, Théorie de Hodge III, Publ. Math. IHES, 44 (1974), 5-27. | Numdam | MR | Zbl

[15] P. Deligne, Interprétation motivique de la conjecture de Zagier reliant polylogarithmes et régulateurs, preprint 1990. | MR

[16] J. Dupont, The dilogarithm as a characteristic class for flat bundles, J. of Pure and Appl. Alg., 44 (1987), 137-164. | MR | Zbl

[17] J. Dupont, Characteristic classes for flat bundles and their formulas, preprint, Aarhus 1993. | MR

[18] J. Dupont, R. Hain, S. Zucker, Regulators and characteristic classes of flat bundles, preprint Aarhus 1992. | MR

[19] J. Dupont, C. H. Sah, Scissors congruences II, Jo. Pure Appl. Alg., 25 (1982), 159-195. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[22] I. M. Gelfand, R. Macpherson, Geometry in grassmannians and a generalization of the dilogarithm, Adv. in Math. 44 (1982), 279-312. | MR | Zbl

[23] W. Gerdes, Affine grassmannian homology and the homology of the general linear groups, Duke Math. J., (1) 62 (1991), 85-103. | MR | Zbl

[24] W. Gerdes, The linearization of higher Chow cycles of dimension one, Duke Math. J., (1) 62 (1991), 105-109. | MR | Zbl

[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. | MR | Zbl

[26] A. B. Goncharov, Geometry of configurations, polylogarithms and motivic cohomology, preprint Max Planck Inst. 1992. | MR

[27] A. B. Goncharov, Polylogarithms and motivic Galois groups, Proc. of the Seattle conf. on motives, Seattle july 1991, preprint. | MR | Zbl

[28] A. B. Goncharov, Explicit construction of characteristic classes, preprint Max Planck Inst. 1992. | MR

[29] S. Govindachar, Explicit weight two motivic cohomology complexes and algebraic K-theory, K-theory, 6 (1992), 387-430. | MR | Zbl

[30] R. Hain, Classical polylogarithms, preprint. | MR

[31] R. Hain, R. Macpherson, Higher logarithms, Illinois J. of Math., 34 (1990), 392-475. | MR | Zbl

[32] M. Hanamura, R. Macpherson, Geometric construction of polylogarithms, Duke Math. J., 70 (1993) 481-515. | MR | Zbl

[33] H. Hiller, $λ$ -ring and algebraic $K$ -theory, J. of Pure and Appl. Alg., 20 (1981), 241-266. | Zbl

[34] W. Hulshergen, Conjectures in arithmetic algebraic geometry, a survey, Aspects of Math., Vieweg 1992. | MR | Zbl

[35] K. Igusa, The Borel regulator map on pictures, preprint.

[36] M. Karoubi, Classes caractéristiques de fibrés feuilletés, holomorphes ou algébriques, preprint Univ. Paris VII, 52 (1993). | MR | Zbl

[37] C. Kratzer, $λ$ -structure en $K$ -théorie algébrique, Comm. Math. Helv., 55 (1980), 233-254. | Zbl

[38] S. Lichtenbaum, The construction of weight two arithmetic cohomology, Inv. Math., 88 (1987), 183-215. | MR | Zbl

[39] J. L. Loday, $K$ -théorie algébrique et représentations de groupes, Ann. Sci. Ec. Norm. Sup., (4) 9 (1976), 309-377. | Numdam | MR | Zbl

[40] J. L. Loday, Symboles en $K$ -théorie algébrique d'ordre supérieur, Comptes rendus Acad. Sci. Paris, 292 (1981), 863-866. | MR | Zbl

[41] J. Milnor, Algebraic $K$ -theory and quadratic forms, Inv. Math., 9 (1970), 318-344. | MR | Zbl

[42] J. Milnor, J. Moore, On the structure of Hopf algebras, Ann. of Math., (2) 81 (1965), 211-264. | MR | Zbl

[43] D. Mumford, Projective invariants of projective structures and applications, Proc. Int. Cong. of Math. 1962, Stockholm, 526-530. | MR | Zbl

[44] J. Oesterlé, Polylogarithmes, Sém. Bourbaki, 762 (1992-93). | Numdam | MR | Zbl

[45] D. Quillen, Higher algebraic $K$ -theory I, Springer Lect. Notes in Math., 341 (1973), 85-197. | MR | Zbl

[46] D. Ramakrishnan, Regulators, algebraic cycles and values of $L$ -functions, Contemp. Math., 83 (1989), 183-310. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[49] Ch. Soulé, Opérations en $K$ -théorie algébrique, Canad. J. of Math., 27 (1985), 488-550. | MR | Zbl

[50] Ch. Soulé, Régulateurs, Sém. Bourbaki 1984/85, exp. 644, Astérique 133/134 (1986), 237-253. | Numdam | MR | Zbl

[51] A. A. Suslin, Homology of $G L_{n}$ , characteristic classes and Milnor $K$ -theory, Springer Lect. Notes in Math., 1046 (1989), 357-375. | MR | Zbl

[52] A. A. Suslin, Algebraic $K$ -theory of fields, Proc. Int. Cong. of Math. 1986, Berkeley, 222-243. | MR | Zbl

[53] A. A. Suslin, $K_{3}$ of a field and the Bloch group, Proc. Steklov inst. of Math., 4 (1991), 217-239. | MR | Zbl

[54] J. Tate, Symbols in Arithmetic, Actes Cong. Int. Nice, 1970, tome 1, 201-211, Gauthier-Villars 1971. | MR | Zbl

[55] B. Totaro, Milnor $K$ -theory is the simplest part of algebraic $K$ -theory, K-theory, 6 (1992), 177-189. | MR | Zbl

[56] W. T. Van Est, Group cohomology and Lie algebra cohomology in Lie groups, Indag. Math., 15 (1953), 484-504. | Zbl

[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. | Numdam | MR | Zbl

[58] J. Yang, The Hain-MacPherson third logarithm, the third Borel regulator and the values of Dedekind zeta function at 3, preprint.

[59] D. Zagier, Hyperbolic manifolds and special values of Dedekind zeta functions, Inv. Math., 83 (1986), 285-301. | MR | Zbl

[60] D. Zagier, Polylogarithms, Dedekind zeta functions and the algebraic $K$ -theory of fields, Proc. Texel Conf. on Arithm. Alg. Geometry 1989, Birkhäuser, Boston (1991), 391-430. | MR | Zbl