Variations of Hodge—de Rham Structure and Elliptic Modular Units

  • Jörg Wildeshaus
Part of the Progress in Mathematics book series (PM, volume 171)


In this paper, we give a conceptual interpretation of generalized elliptic units in terms of variations of Hodge-de Rham structure, and of (elliptic) polylogarithms.


Modulus Space Elliptic Curve Base Change Elliptic Curf Multivalued Function 
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  1. [BD]
    A.A. Beilinson, P. Deligne, Interprétation motivique de la conjecture de Zagier reliant polylogarithmes et régulateurs, in Motives, U. Jannsen, S.L. Kleiman, J.-P. Serre, eds., Proc. of Symp. in Pure Math. 55, Part II, AMS, 1994, pp. 123–190.Google Scholar
  2. [CKS]
    E. Cattani, A. Kaplan, W. Schmid, Degeneration of Hodge structures, Ann. of Math. 123 (1986), 457–535.MathSciNetMATHCrossRefGoogle Scholar
  3. [D]
    P. Deligne, Equations Différentielles à Points Singuliers Réguliers, LNM 163, Springer-Verlag, 1970.Google Scholar
  4. [DM]
    P. Deligne, J.S. Milne, Tannakian categories, in Hodge Cycles, Motives, and Shimura Varieties, P. Deligne, J.S. Milne, A. Ogus, K.-y. Shih, eds., LNM 900, Springer-Verlag, 1982, 101–228.CrossRefGoogle Scholar
  5. [GL]
    A. Goncharov, A. Levin, Zagier’s conjecture on L(E, 2), Invent. Math. 132 (1998), 393–432.MathSciNetMATHCrossRefGoogle Scholar
  6. [H]
    M. Harris, Hodge—de Rham structures and periods of automorphic forms, in Motives, U. Jannsen, S.L. Kleiman, J.-P. Serre, eds., Proc. of Symp. in Pure Math. 55, Part II, AMS, 1994, 573–624.Google Scholar
  7. [Ka]
    M. Kashiwara, A study of variation of mixed Hodge structure, Publ. RIMS Kyoto Univ. 22 (1986), 991–1024.MathSciNetMATHCrossRefGoogle Scholar
  8. [KL]
    [ D.S. Kubert, S. Lang, Modular units, Grundlehren Math. Wiss. 244, Springer-Verlag, 1981.Google Scholar
  9. [Ku]
    D.S. Kubert, Product formulae on elliptic curves, Invent. Math. 117 (1994), 227–273.MathSciNetMATHCrossRefGoogle Scholar
  10. [L]
    S. Lang, Elliptic Functions, Addison—Wesley, Reading, MA, 1973.MATHGoogle Scholar
  11. [R]
    K. Rolshausen, Eléments explicites dans К 2 d’une courbe elliptique, thèse, Prépubl ications de l’Institut de Recherche Mathématiques avancée 1996/05.Google Scholar
  12. [dSh]
    E. de Shalit, Iwasawa Theory of Elliptic Curves with Complex Multiplication, Perspectives in Math. 3, Academic Press, 1987.MATHGoogle Scholar
  13. [Si]
    J.H. Silverman, Advanced Topics in the Arithmetic of Elliptic Curves, GTM 151, Springer-Verlag, 1994.MATHCrossRefGoogle Scholar
  14. [W1]
    J. Wildeshaus, Realizations of Polylogarithms, LNM 1650, Springer-Verlag, 1997.Google Scholar
  15. [W1IV]
    J. Wildeshaus, Polylogarithmic extensions on mixed Shimura varieties. Part II: The classical polylogarithm, in [W1, 199–248].Google Scholar
  16. [W1V]
    J. Wildeshaus, Polylogarithmic extensions on mixed Shimura varieties. Part III: The elliptic polylogarithm, in [W1, 249–340].Google Scholar
  17. [W2]
    J. Wildeshaus, On an elliptic analogue of Zagier’s conjecture, Duke Math. J. 87 (1997), 355–407.MathSciNetMATHCrossRefGoogle Scholar
  18. [W3]
    J. Wildeshaus, On the generalized Eisenstein symbol, in Motives, Polylogarithms, and Nonabelian Hodge Theory; Proceedings of the conference held June 4–6 1988 at the University of California at Irvine, to appear.Google Scholar

Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Jörg Wildeshaus
    • 1
  1. 1.Institut GaliléeUniversité ParisVilletaneuseFrance

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