Polylogarithms, regulators, and arakelov motivic complexes

Journal of the American Mathematical Society

Volumn 18, Issue 1, 2005, Pages 1-60

  Goncharov, A B ^a  

^a BROWN UNIVERSITY   (United States)

Author keywords

Arakelov theory; Motivic complexes; Polylogarithms; Regulators

Indexed keywords

EID: 13644250307     PISSN: 08940347     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0894-0347-04-00472-2     Document Type: Article

References (45)

1. [B11] Bloch S.: Algebraic cycles and higher K-theory, Adv. in Math., (1986), v. 61, 267-304. MR0852815 (88f:18010)
2. [B12] Bloch S.: The moving lemma for higher Chow groups, J. Alg. Geometry 3 (1994). MR1269719 (96c:14007)
3. [B13] Bloch S.: Algebraic cycles and the Beilinson conjectures, Contemp. Math. 58 (1986) no 1, 65-79. MR0860404 (88e:14006)
4. [BK] Bloch S., Kriz I.: Mixed Tate motives, Ann. of Math., 140 (1994) vol. 3, 557-605, 1992. MR1307897 (96c:11062); MR1307897 (96c:11062)
5. [Bo1] Borel A.: Stable real cohomology of arithmetic groups, Ann. Sci. EC. Norm. Super., (4) 7 (1974), 235-272. MR0387496 (52:8338)
6. n et valeurs de fonctions zêta aux points entiers, Ann. Sc. Norm. Sup. Pisa 4 (1977), 613-636. MR0506168 (58:22016)
7. [Bott] Bott R.: On the characteristic classes of groupa of diffeomorphisms, Ensiegnment Mathématique, T. XXIII, fsc. 3-4 (1977) 209-220. MR0488080 (58:7651)
8. [Bu] Burgos, J. I.: Arithmetic Chow rings and Deligne-Beilinson cohomology, 3. Algebraic Geom. 6 (1997), no. 2, 335-377. MR1489119 (99d:14015)
9. [C] Consani C.: Double complexes and Euler's L-factors, Compositio Math. 111 (1998) 323-358. MR1617133 (99b:11065)
10. [D] Dupont J.: Simplicial de Rham cohomolgy and characteristic classes of flat bundles, Topology 15 (1976), 233-245. MR0413122 (54:1243)
11. [Del] Deligne, P.: Le déterminant de la cohomologie. Current trends in arithmetical algebraic geometry (Arcata, Calif., 1985), 93-177, Contemp. Math., 67, Amer. Math. Soc., Providence, RI, 1987. MR0902592 (89b:32038)
12. [F] Fulton W.: Intersection theory. Second edition. Springer 1998. MR1644323 (99d:14003)
13. [Dyn] Dynkin E.B.: Topological characteristics of compact Lie groups homomorphisms, Math. Sb. NS 35 (1954), 129-173. MR0067124 (16:673b)
14. [GGL] Gabrielov A., Gelfand I.M., Losik M.: Combinatorial computation of characteristic classes I, II, Funkt. Anal, i Pril. 9 (1975) 12-28, ibid 9 (1975) 5-26. MR0410758 (53:14504a)
15. [GGL] Gabrielov A., Gelfand I.M., Losik M.: Combinatorial computation of characteristic classes I, II, Funkt. Anal, i Pril. 9 (1975) 12-28, ibid 9 (1975) 5-26. MR0410758 (53:14504a)
16. [GM] Gelfand I.M., MacPherson R.: Geometry in Grassmannians and a generalisation of the diluogarithm, Adv. in Math., 44 (1982) 279-312. MR0658730 (84b:57014)
17. [GS] Gillet, H.; Soulé, C.: Arithmetic intersection theory, Inst. Hautes Études Sci. Publ. Math. No. 72, (1990), 93-174 (1991). MR1087394 (92d:14016)
18. [G1] Goncharov A.B.: Geometry of configurations, polylogarithms and motivic cohomology, Adv. in Math., 114, (1995), 197-318. MR1348706 (96g:19005)
19. [G2] Goncharov A.B.: Polylogarithms and motivic Galois groups in Symp. in Pure Math., v. 55, part 2, 1994, 43 - 97. MR1265551 (94m:19003)
20. [G3] Goncharov A.B.: Explicit construction of characteristic classes, I.M. Gelfand seminar Adv. Soviet Math., 1993, v. 16, 169-210. MR1237830 (95c:57045)
21. [G4] Goncharov, A.B.: Deninger's conjecture on special values of L-functions of elliptic curves at s = 3, J. Math. Sci. 81 (1996), N3, 2631-2656, alg-geom/9512016. MR1420221 (98c:19002)
22. [G5] Goncharov A.B.: Chow polylogarithms and regulators. Math. Res. Letters, 2, (1995), 99-114. MR1312980 (96b:19007)
23. [G6] Goncharov, A.B.: Geometry of trilogarithm and the motivic Lie algebra of a field, Regulators in analysis, geometry and number theory, 127-165, Progr. Math., 171, Birkhäuser Boston, Boston, MA, 2000. math.AG/0011168. MR1724890 (2000j:11096)
24. [G7] Goncharov, A.B.: Explicit regulator maps on the polylogarithmic motivic complexes, Motives, polylogarithms and Hodge theory, Part I (Irvine, CA, 1998), 245-276, Int. Press Lect. Ser., 3, I, Int. Press, Somerville, MA, 2002. math.AG/0003086. MR1978709 (2004b:11095)
25. [GZ] Goncharov A.B., Zhao J.: The Grassmannian trilogarithms. Compositio Math. 127 (2001), no. 1, 83-108. math.AG/0011165. MR1832988 (2002g:33004)
26. [HM] Hain R., MacPherson R.: Higher Logarithms, Ill. J. of Math., vol. 34, (1990) N2, 392-475. MR1046570 (92c:14016)
27. [H] Hain R.: The existence of higher logarithms. Compositio Math. 100 (1996) N3, 247-276. MR1387666 (97g:19008)
28. [HY] Hain R., Yang R.: Real Grassmann polylogarithms and Chern classes. Math. Annalen, 304, (1996), N1, 157-201. MR1367888 (96k:19007)
29. [HM1] Hanamura M., MacPherson R.: Geometric construction of polylogarithms, Duke Math. J. 70 (1993) 481-516. MR1224097 (94h:19005)
30. [HM2] Hanamura M., MacPherson R.: Geometric construction of polylogarithms, II, Progress in Math. vol. 132 (1996) 215-282. MR1389020 (97g:19007)
31. [Lei] Gerhardt C.I. (ed). G.W.Leibniz Mathematische Schriften III/1 pp. 336-339 Georg Olms Verlag, Hildesheim. New York 1971. MR0141576 (25:4979b)
32. [Le] Levin A.M.: Notes on ℝ-Hodge-Tate sheaves. Preprint MPI 2001.
33. [Lev] Levine, M.: Block's higher Chow groups revisited. K-theory. Astérisque No. 226 (1994), 10, 235-320. MR1317122 (96c:14008)
34. [Li] Lichtenbaum S.: Values of zeta functions at non-negative integers, Lect. Notes in Math., 1068, Springer-Verlag, 1984, 127-138. MR0406981 (53:10765)
35. [M] MacPherson R.: Gabrielov, Gelfand, Losik combinatorial formula for the first Pontrjagin class Seminar Bourbaki 1976. MR0521763 (81a:57022)
36. [N] Nekovář J.: Beilinson's conjectures. Motives (Seattle, WA, 1991), 537-570, Proc. Sympos. Pure Math., 55, Part 1, Amer. Math. Soc., Providence, RI, 1994. MR1265544 (95f:11040)
37. [N] Nekovář J.: Beilinson's conjectures. Motives (Seattle, WA, 1991), 537-570, Proc. Sympos. Pure Math., 55, Part 1, Amer. Math. Soc., Providence, RI, 1994. MR1265544 (95f:11040)
38. [NS] Nesterenko Yu.P., Suslin A.A.: Homology of the general linear group over a local ring, and Milnor's K-theory. Math. USSR-Izv. 34 (1990), no. 1, 121-142. MR0992981 (90a:20092)
39. [RSS] Rapoport M., Schappacher N., Schneider P.: Beilinson's conjectures on special values of L-functions. Perspectives in Mathematics, 4. Academic Press, Inc., Boston, MA, 1988. MR0944987 (89a:14002)
40. [Seh] Scholl A.: Integral elements in K-theory and products of modular curves. The arithmetic and geometry of algebraic cycles (Banff, AB, 1998), 467-489, NATO Sci. Ser. C Math. Phys. Sci., 548. MR1744957 (2001i:11077)
41. [Seh] Scholl A.: Integral elements in K-theory and products of modular curves. The arithmetic and geometry of algebraic cycles (Banff, AB, 1998), 467-489, NATO Sci. Ser. C Math. Phys. Sci., 548. MR1744957 (2001i:11077)
42. [S] Soulé C., Abramovich D., Burnol J. F., Kramer, J. K.: Lectures on Arakelov geometry. Cambridge University Press, 1992. MR1208731 (94e:14031)
43. n, characteristic classes and Milnor's K-theory. Lect. Notes in Math. 1046 (1989), 357-375. MR0752941 (86f:11090b)
44. [Z1] Zagier D: Polylogarithms, Dedekind zeta functions and the algebraic K-theory of fields, Arithmetic Algebraic Geometry (G.v.d.Geer, F.Oort, J.Steenbrink, eds.), Prog. Math., Vol 89, Birkhäuser, Boston, 1991, pp. 391-430. MR1085270 (92f:11161)
45. [Z1] Zagier D: Polylogarithms, Dedekind zeta functions and the algebraic K-theory of fields, Arithmetic Algebraic Geometry (G.v.d.Geer, F.Oort, J.Steenbrink, eds.), Prog. Math., Vol 89, Birkhäuser, Boston, 1991, pp. 391-430. MR1085270 (92f:11161)