Groupes fondamentaux motiviques de Tate mixte

Deligne, Pierre; Goncharov, Alexander B.

doi:10.1016/j.ansens.2004.11.001

Deligne, Pierre ; Goncharov, Alexander B.

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 38 (2005) no. 1, pp. 1-56.

MR Zbl | 6 citations dans Numdam

DOI : 10.1016/j.ansens.2004.11.001

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Deligne, Pierre; Goncharov, Alexander B. Groupes fondamentaux motiviques de Tate mixte. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 38 (2005) no. 1, pp. 1-56. doi : 10.1016/j.ansens.2004.11.001. http://archive.numdam.org/articles/10.1016/j.ansens.2004.11.001/

Bibliographie
Cité par

[1] Bass H., Generators and relations for cyclotomic units, Nagoya Math. J. 27 (1966) 401-407. | MR | Zbl

[2] Beilinson A., Higher regulators and values of L-functions, Sovremennye Problemy Matematiki 24 (1984) 181-238, (en russe). | MR | Zbl

[3] Beilinson A., Bernstein J., Deligne P., Faisceaux pervers, in: Analyse et topologie sur les espaces singuliers, Astérisque, vol. 100, SMF, 1982. | MR | Zbl

[4] Bloch S., Algebraic cycles and algebraic K-theory, Adv. in Math. 61 (3) (1986) 267-304. | MR | Zbl

[5] Bloch S., The moving lemma for higher Chow groups, J. Algebraic Geom. 3 (3) (1994) 537-568. | MR | Zbl

[6] Borel A., Stable real cohomology of arithmetic groups, Ann. Sci. Éc. Nom. Sup. 7 (1974) 235-272. | Numdam | MR | Zbl

[7] Borel A., Cohomologie de ${SL}_{n}$ et valeurs de fonctions zêta aux points entiers, Ann. Scuola Normale Superiore 4 (1977) 613-636. | Numdam | MR | Zbl

[8] Buchsbaum A., Satellites and exact functors, Ann. of Math. 71 (2) (1960) 199-209. | MR | Zbl

[9] Chen K.T., Iterated integrals of differential forms and loop space homology, Ann. of Math. 97 (1973) 217-246. | MR | Zbl

[10] Chen K.T., Reduced Bar Constructions on de Rham complexes, in: Algebra, Topology and Category Theory, a collection of papers in honor of Samuel Eilenberg, Academic Press, 1976, pp. 19-32. | MR | Zbl

[11] Deligne P., Le groupe fondamental de la droite projective moins trois points, in: Galois Groups over $Q$ , MSRI Publ., vol. 16, Springer-Verlag, 1989, pp. 79-313. | MR | Zbl

[12] Deligne P., Catégories tannakiennes, in: Grothendieck Festschrift, vol. 2, Progress in Math., vol. 87, Birkhäuser, 1990, pp. 111-195. | MR | Zbl

[13] Deligne P., Morgan J., Notes on supersymmetry, in: Quantum Fields and Strings : A Course for Mathematicians, vol. 1, AMS, 1999. | MR | Zbl

[14] Demazure M., Gabriel P., Groupes algébriques, Masson, 1970.

[15] Goncharov A.B., Polylogarithms in arithmetic and geometry, in: Proc. ICM Zurich, Birkhäuser, 1994, pp. 374-387. | MR | Zbl

[16] Goncharov A.B., The dihedral Lie algebras and Galois symmetries of $π_{1} (P^{1} - {0, \infty} \cup μ_{N})$ , Duke Math. J. 110 (3) (2001) 397-487. | MR | Zbl

[17] Hain R., Matsumoto M., Weighted completion of Galois groups and Galois actions on the fundamental group of $P^{1} - {0, 1, \infty}$ , Compositio Math. 139 (2) (2003) 119-167. | MR | Zbl

[18] Hain R., Zucker S., Unipotent variations of mixed Hodge structure, Inv. Math. 88 (1987) 83-124. | MR | Zbl

[19] Hanamura M., Mixed motives and algebraic cycles I, Math. Res. Lett. 2 (6) (1995) 811-821, See also II, Inv. Math. 158 (1) (2004) 105-179. | MR | Zbl

[20] Huber A., Mixed Motives and their Realization in Derived Categories, Lecture Notes in Math., vol. 1604, Springer-Verlag, 1995. | MR | Zbl

[21] Huber A., Realization of Voevodsky's motives, J. Algebraic Geom. 9 (2000) 755-799, Corrigendum, Ibid. 13 (1) (2004) 195-207. | MR | Zbl

[22] Jannsen U., Mixed Motives and Algebraic K-Theory, Lecture Notes in Math., vol. 1400, Springer-Verlag, 1990. | MR | Zbl

[23] Kubert D., The universal ordinary distribution, Bull. SMF 107 (1979) 79-202. | Numdam | MR | Zbl

[24] Levine M., Tate motives and the vanishing conjectures for algebraic K-theory, in: Algebraic K-Theory and Algebraic Topology, Lake Louise, 1991, NATO Adv. Sci. Inst. Ser. C Math. Phys., vol. 407, Kluwer, 1993, pp. 167-188. | MR | Zbl

[25] Levine M., Bloch's higher Chow groups revisited, in: K-theory, Strasbourg, 1992, Astérisque, vol. 226, SMF, 1994, pp. 235-320. | Numdam | MR | Zbl

[26] Levine M., Mixed Motives, Math. Surveys and Monographs, vol. 57, AMS, 1998. | MR | Zbl

[27] Racinet G., Doubles mélanges des polylogarithmes multiples aux racines de l'unité, Publ. Math. IHÉS 95 (2002) 185-231. | Numdam | MR | Zbl

[28] Rapoport M., Comparison of the regulators of Beilinson and of Borel, in: Beilinson's Conjectures on Special Values of L-Functions, Perspectives in Math., vol. 4, Academic Press, 1988, pp. 169-192. | MR | Zbl

[29] Reutenauer C., Free Lie Algebras, LMS Monographs New Ser., vol. 7, Oxford University Press, 1993. | MR | Zbl

[30] Schneider P., Introduction to the Beilinson conjectures, in: Beilinson's Conjectures on Special Values of L-Functions, Perspectives in Math., vol. 4, Academic Press, 1988, pp. 1-35. | MR | Zbl

[31] Terasoma T., Multiple zeta values and mixed Tate motives, Inv. Math. 149 (2) (2002) 339-369. | MR | Zbl

[32] Voevodsky V., Triangulated categories of motives over a field, in: Cycles, Transfer and Motivic Homology Theories, Ann. of Math. Studies, vol. 143, Princeton University Press, 2000, pp. 188-238. | MR | Zbl

[33] Washington L.C., Introduction to cyclotomic fields, Graduate Texts in Math., vol. 81, Springer-Verlag, 1997. | MR | Zbl

[34] Wojtkowiak Z., Cosimplicial objects in algebraic geometry, in: Algebraic K-Theory and Algebraic Topology, Lake Louise, 1991, NATO Adv. Sci. but. Ser. C Math. Phys., vol. 407, Kluwer, 1993, pp. 287-327. | MR | Zbl

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