Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-22T17:27:24.915Z Has data issue: false hasContentIssue false
  • English
  • Français

The motivic fundamental group of the punctured projective line

Published online by Cambridge University Press:  07 April 2010

Bertrand J. Guillou
Bertrand J. Guillou
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, IL 61801, U.S.A, [email protected]
Get access

Abstract

We describe a construction of an object associated to the fundamental group of ℙ1 − {0, 1, ∞} in the Bloch-Kriz category of mixed Tate motives. This description involves Massey products in the motivic cohomology of the ground field.

Keywords

Motive π1mixed Tate motive
Type
Research Article
Information
Journal of K-Theory , Volume 7 , Issue 1 , February 2011 , pp. 19 - 53
Copyright
Copyright © ISOPP 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

BBD.Beĭlinson, A. A., Bernstein, J., and Deligne, P.. Faisceaux pervers. In Analysis and topology on singular spaces, I (Luminy, 1981),Astérisque 100:5–171, 1982.Google Scholar
BK1.Bloch, Spencer and Kříž, Igor. Mixed Tate motives. Ann. of Math. (2), 140(3):557–605, 1994.CrossRefGoogle Scholar
BK2.Bondal, A. I. and Kapranov, M. M.. Framed triangulated categories. Mat. Sb. 181(5):669–683, 1990.Google Scholar
Blo1.Bloch, Spencer. Algebraic cycles and higher K-theory. Adv. in Math. 61(3):267–304, 1986.CrossRefGoogle Scholar
Blo2.Bloch, Spencer. Algebraic cycles and the Lie algebra of mixed Tate motives. J. Amer. Math. Soc. 4(4):771–791, 1991.CrossRefGoogle Scholar
Blo3.Bloch, Spencer. Letter to H.Esnault and M.Levine. December 2006.Google Scholar
Bor.Borel, Armand. Stable real cohomology of arithmetic groups. Ann. Sci. École Norm. Sup. (4), 7:235–272 (1975), 1974.CrossRefGoogle Scholar
Del.Deligne, P.. Le groupe fondamental de la droite projective moins trois points. In Galois groups over Q (Berkeley, CA, 1987), Math. Sci. Res. Inst. Publ. 16:79–297, 1989.Google Scholar
DG.Deligne, Pierre and Goncharov, Alexander B.. Groupes fondamentaux motiviques de Tate mixte. Ann. Sci. École Norm. Sup. (4), 38(1):1–56, 2005.CrossRefGoogle Scholar
EL.Esnault, H. and Levine, M.. Tate motives and the fundamental group. Arxiv preprint arXiv:0708.4034, 2007.Google Scholar
FJ.Furusho, Hidekazu and Jafari, Amir. Algebraic cycles and motivic generic iterated integrals. Math. Res. Lett. 14(6):923–942, 2007.CrossRefGoogle Scholar
FS.Friedlander, Eric M. and Suslin, Andrei. The spectral sequence relating algebraic K-theory to motivic cohomology. Ann. Sci. École Norm. Sup. (4), 35(6):773–875, 2002.CrossRefGoogle Scholar
FV., Eric M., Friedlander and Voevodsky, Vladimir. Bivariant cycle cohomology. In Cycles, transfers, and motivic homology theories, Ann. of Math. Stud. 143:138–187, 2000.Google Scholar
GGL.Gangl, H., Goncharov, A.B., and Levin, A.. Multiple polylogarithms, polygons, trees and algebraic cycles. Arxiv preprint math.NT/0508066, 2005.Google Scholar
GM.Gelfand, Sergei I. and Manin, Yuri I.. Methods of homological algebra. Springer Monographs in Mathematics. Springer-Verlag, Berlin, second edition, 2003.Google Scholar
Jaf.Jafari, A.. Algebraic cycles and motivic iterated integrals II. Arxiv preprint arXiv: 0806.4637, 2008.Google Scholar
KM.Kříž, Igor and May, J. P.. Operads, algebras, modules and motives. Astérisque 233:iv+145pp, 1995.Google Scholar
Lev.Levine, Marc. Mixed motives. In >Handbook of K-theory. Vol. 1, 2, pages 429-521. Springer, Berlin, 2005.CrossRefGoogle Scholar
May.May, J. P.. Matric Massey products. J. Algebra 12:533–568, 1969.CrossRefGoogle Scholar
MVW.Mazza, Carlo, Voevodsky, Vladimir and Weibel, Charles. Lecture notes on motivic cohomology, Clay Mathematics Monographs, 2, American Mathematical Society, Providence, RI, 2006.Google Scholar
NS.Nesterenko, Yu. P. and Suslin, A. A.. Homology of the general linear group over a local ring, and Milnor's K-theory. Izv. Akad. Nauk SSSR Ser. Mat. 53(1):121-146, 1989.Google Scholar
Sus.Suslin, Andrei A.. Higher Chow groups and etale cohomology. In Cycles, transfers, and motivic homology theories, Ann. of Math. Stud. 143:239–254, 2000.Google Scholar
Tot.Totaro, Burt. Milnor K-theory is the simplest part of algebraic K-theory. K-Theory 6(2):177–189, 1992.CrossRefGoogle Scholar