Galois symmetries of fundamental groupoids and noncommutative geometry

Duke Mathematical Journal

Volumn 128, Issue 2, 2005, Pages 209-284

  Goncharov, A B ^a  

^a BROWN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22544437289     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-04-12822-2     Document Type: Article

References (28)

1. [BD] A. A. BEILINSON and P. DELIGNE, Motivic poly logarithms and Zagier's conjecture, unpublished manuscript, version of 1992.
2. [BGSV] A. A. BEILINSON, A. B. GONCHAROV, V. V. SCHECHTMAN, and A. N. VARCHENKO, "Aomoto dilogarithms, mixed Hodge structures and motivic cohomology of pairs of triangles on the plane" in The Grothendieck Festschtrift, Vol. I, Progr. Math. 86, Birkhäuser, Boston, 1990, 135-172. MR 1086885
3. [BB] P. BELKALE and P. BROSNAN, Matroids, motives, and a conjecture of Kontsevich, Duke Math. J. 116 (2003), 147-188. MR 1950482
4. n et valeurs de fonctions zeta aux points entiers, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 4 (1977), 613-636; Errata, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 7 (1980), 373. MR 0506168; MR 05881146
5. [BGK] D. J. BROADHURST, J. A. GRACEY, and D. KREIMER, Beyond the triangle and uniqueness relations: Non-zeta counterterms at large N from positive knots, Z. Phys. C 75 (1997), 559-574. MR 1461268
6. [C] K. T. CHEN, Iterated path integrals. Bull. Amer. Math. Soc. 83 (1977), 831-879. MR 0454968
7. [CK] A. CONNES and D. KREIMER, Hopf algebras, renormalization and noncommutative geometry, Comm. Math. Phys. 199 (1998), 203-242. MR 1660199
8. [D1] P. DELIGNE, "Le groupe fondamental de la droite projective moins trois points" in Galois Groups over Q (Berkeley, 1987), Math. Sci Res. Inst. Publ. 16, Springer, New York, 1989, 79-297. MR 1012168
9. [D2] _, "Catégories tannakiennes" in The Grothendieck Festschrift, Vol. H, Progr. Math. 87, Birkhäuser, Boston, 1990, 111-195. MR 1106898
10. [DG] P. DELIGNE and A. B. GONCHAROV, Groupes fondamentaux motiviques de Tate mixte, Ann. Sci. École Norm Sup. (4), 38 (2005), 1-56.
11. [Dr] V. G. DRINFELD, On quasitriangular quasi-Hopf algebras and on a group that is closely connected with Gal(ℚ/ℚ) (in Russian), Algebra i Analiz 2, no. 4 (1990), 149-181;
12. English translation in Leningrad Math. J. 2 (1991), 829-860. MR 1080203
13. [G1] A. B. Goncharov, "Polylogarithms and motivic Galois groups" in Motives (Seattle, 1991), Proc. Sympos. Pure Math. 55, Part 2, Amer. Math. Soc., Providence, 1994, 43-96. MR 1265551
14. [G2] _, "Polylogarithms in arithmetic and geometry" in Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994), Birkhäuser, Basel, 1995, 374-387. MR 1403938
15. [G3] _, "Mixed elliptic motives" in Galois representations in Arithmetic Algebraic Geometry, (Durham, 1996), London Math. Soc. Lecture Note Ser. 254, Cambridge Univ. Press, Cambridge, 1998, 147-221. MR 1696477
16. [G4] _, Multiple polylogarithms, cyclotomy and modular complexes, Math. Res. Lett. 5 (1998), 497-516. MR 1653320
17. [G5] _, Volumes of hyperbolic manifolds and mixed Tate motives, J. Amer. Math. Soc. 12 (1999), 569-618. MR 1649192
18. N), Duke Math. J. 110 (2001), 397-487. MR 1869113
19. [G7] _, "Multiple ζ-values, Galois groups, and geometry of modular varieties" in European Congress of Mathematics, Vol. I (Barcelona, 2000), Progr. Math. 201, Birkhäuser, Basel, 2001, 361-392. MR 1905330
20. [G8] _, Multiple ζ-numbers, hyperlogarithms and mixed Tate motives, preprint, June 1993, Mathematical Sciences Research Institute, Berkeley, no. 058-93.
21. [G9] _, Galois groups, geometry of modular varieties and graphs, Proceedings of Arbeitstagung, June 1999, preprint, no. MPIM1999-50f, http://www.mpim-bonn.mpg.de
22. [G10] _, Multiple polylogarithms and mixed Tate motives, preprint, arXiv:math.AG/0103059
23. [G11] _, Periods and mixed motives, preprint, arXiv:math.AG/0202154
24. [K] D. KREIMER, On the Hopf algebra structure of perturbative quantum field theories, Adv. Theor. Math. Phys. 2 (1998), 303-334. MR 1633004
25. [L] M. LEVINE, "Tate motives and the vanishing conjectures for algebraic K-theory" in Algebraic K-Theory and Algebraic Topology (Lake Louise, Canada, 1991), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 407, Kluwer, Dordrecht, 1993, 167-188. MR 1367296
26. [Lo1] J.-L. LODAY, "Dialgebras" in Dialgebras and Related Operads, Lecture Notes in Math. 1763, Springer, Berlin, 2001, 7-66. MR 1860994
27. [Lo2] _, Arithmetree, J. Algebra 258 (2002), 275-309. MR 1958907
28. [Z] D. ZAGIER, "Periods of modular forms, traces of Hecke operators, and multiple zeta values" in Research into Automorphic Forms and L Functions (Kyoto, 1992) (in Japanese), Sürikaisekikenkyüsho Kōkyūroku 843, Kyoto Univ., Kyoto, 1993, 162-170. MR 1296720