On a generalization of Hilbert's 21st problem

Richard M. Hain

Annales scientifiques de l'École Normale Supérieure (1986)

  • Volume: 19, Issue: 4, page 609-627
  • ISSN: 0012-9593

How to cite


Hain, Richard M.. "On a generalization of Hilbert's 21st problem." Annales scientifiques de l'École Normale Supérieure 19.4 (1986): 609-627. <http://eudml.org/doc/82189>.

author = {Hain, Richard M.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {monodromy representation; mixed Hodge structure},
language = {eng},
number = {4},
pages = {609-627},
publisher = {Elsevier},
title = {On a generalization of Hilbert's 21st problem},
url = {http://eudml.org/doc/82189},
volume = {19},
year = {1986},

AU - Hain, Richard M.
TI - On a generalization of Hilbert's 21st problem
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1986
PB - Elsevier
VL - 19
IS - 4
SP - 609
EP - 627
LA - eng
KW - monodromy representation; mixed Hodge structure
UR - http://eudml.org/doc/82189
ER -


  1. [1] K. AOMOTO, Fonctions hyperlogarithmiques et groupes de monodromie unipotents (J. Fac. Sci. Tokyo, Vol. 25, 1978, pp. 149-156). Zbl0416.32020MR80g:14016
  2. [2] G. D. BIRKHOFF, The generalized Riemann Problem, Collected Mathematical Papers, American Mathematical Society, New York, 1950. 
  3. [3] L. BOUTET DE MONVEL, A. DOUADY and J.-L. VERDIER, Mathématique et Physique, Birkhöuser, Boston, 1983. Zbl0516.00021MR84m:32001
  4. [4] K.-T. CHEN, Extension of C∞ function algebra by integrals and Malcev completion of π1 (Advances in Math., Vol. 23, 1977, pp. 181-210). Zbl0345.58003MR56 #16664
  5. [5] K.-T. CHEN, Iterated path integrals (Bull. Amer. Math. Soc., Vol. 83, 1977, pp. 831-879). Zbl0389.58001MR56 #13210
  6. [6] D. CHUDNOVSKY and G. CHUDNOVSKY, editors, The Riemann Problem, Complete Integrability, and Arithmetic Applications (Lecture Notes in Mathematics 925, Springer-Verlag, Berlin, Heidelberg, New York, 1982). Zbl0477.00009MR83f:81003
  7. [7] P. DELIGNE, Équations Différentielles à Points Singuliers Réguliers (Lecture Notes in Mathematics 163, Springer-Verlag, Berlin, Heidelberg, New York, 1970. Zbl0244.14004MR54 #5232
  8. [8] P. DELIGNE, Théorie de Hodge II (Publ. Math. IHES, No. 40, 1971, pp. 5-58). Zbl0219.14007MR58 #16653a
  9. [9] V. GOLUBEVA, On the recovery of Pfaffian systems of Fuchsian type from the generators of the monodromy group (Math. USSR. Izvestija, Vol. 17, 1981, pp. 227-241). Zbl0494.58003
  10. [10] R. HAIN, The de Rham homotopy theory of complex algebraic varieties, (preprint). Zbl0637.55006
  11. [11] R. HAIN, The geometry of the mixed Hodge structure on the fundamental group, Algebric geometry 1985, Proc. Symp. Rire Math., to appear. 
  12. [12] D. HILBERT, Mathematical Problems, Lecture delivered before the International Congress of Mathematicians at Paris in 1900, reproduced in : Mathematical Developments Arising from Hilbert Problems (Proc. Symp. Pure Math., Vol. 28, American Math. Soc., 1976). 
  13. [13] J. HUMPHREYS, Linear Algebraic Groups, Springer-Verlag, New York, 1975. Zbl0325.20039MR53 #633
  14. [14] S.-Y. HWANG-MA, Periods of iterated integrals of holomorphic forms on a compact Riemann surface (Trans. Amer. Math. Soc., Vol. 264, 1981, pp. 295-300). Zbl0478.32016MR82k:14025
  15. [15] N. KATZ, An overview of Delign's work on Hilbert's twenty first problem (Proc. Symp. Pure Math., Vol. 28, Amer. Math. Soc., Providence, R. I., 1976, pp. 537-557). Zbl0347.14010MR55 #5627
  16. [16] I. A. LAPPO-DANILEVSKY, Mémoires sur la théorie des systèmes des équations différentielles linéaires, reprint, Chelsea, New York, 1953. Zbl0051.32301
  17. [17] J. MORGAN, The algebraic topology of smooth algebraic varieties (Publ. IHES, No. 48, 1978, pp. 137-204). Zbl0401.14003MR80e:55020
  18. [18] R. NARASIMHAN, Analysis on Real and Complex Manifolds, North Holland, Amsterdam, London, New York, 1973. MR49 #11576
  19. [19] D. PASSMAN, The Algebraic Theory of Group Rings, John Wiley, New York, 1977. Zbl0368.16003
  20. [20] J. PLEMELJ, Problems in the Sense of Riemann and Klein, John Wiley, New York, 1964. Zbl0124.28203MR30 #5008
  21. [21] D. QUILLEN, Rational homotopy theory (Ann. Math., Vol. 90, 1969, pp. 205-295). Zbl0191.53702MR41 #2678

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.