The existence of higher logarithms

Richard M. Hain

Compositio Mathematica (1996)

  • Volume: 100, Issue: 3, page 247-276
  • ISSN: 0010-437X

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Hain, Richard M.. "The existence of higher logarithms." Compositio Mathematica 100.3 (1996): 247-276. <http://eudml.org/doc/90429>.

@article{Hain1996,
author = {Hain, Richard M.},
journal = {Compositio Mathematica},
keywords = {higher logarithms; Deligne cohomology; Chern classes; functional equation},
language = {eng},
number = {3},
pages = {247-276},
publisher = {Kluwer Academic Publishers},
title = {The existence of higher logarithms},
url = {http://eudml.org/doc/90429},
volume = {100},
year = {1996},
}

TY - JOUR
AU - Hain, Richard M.
TI - The existence of higher logarithms
JO - Compositio Mathematica
PY - 1996
PB - Kluwer Academic Publishers
VL - 100
IS - 3
SP - 247
EP - 276
LA - eng
KW - higher logarithms; Deligne cohomology; Chern classes; functional equation
UR - http://eudml.org/doc/90429
ER -

References

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  1. 1 Beilinson, A.: Higher regulators and values of L-functions of curves, Func. Anal. and its Appl. 14 (1980), 116-118. Zbl0475.14015MR575206
  2. 2 Beilinson, A.: Notes on absolute Hodge cohomology in Applications of Algebraic K-Theory to Algebraic Geometry and Number Theory, Contemporary Math. 55, part I, Amer. Math. Soc., Providence, 1986, 35-68. Zbl0621.14011MR862628
  3. 3 Beilinson, A., MacPherson, R., and Schechtman, V.: Notes on motivic cohomology, Duke Math. J.54 (1987), 679-710. Zbl0632.14010MR899412
  4. 4 Bloch, S.: Higher regulators, Algebraic K-theory, and zeta functions of elliptic curves, unpublished manuscript, 1978. 
  5. 5 Carlson, J. and Hain, R.: Extensions of Variations of Mixed Hodge Structure, Théorie de Hodge, Luminy, Juin, 1987, Astérisque no. 179-180, 39-65. Zbl0717.14004MR1042801
  6. 6 Dupont, J.: The dilogarithm as a characteristic class for flat bundles, J. Pure and App. Alg.44 (1987), 137-164. Zbl0624.57024MR885101
  7. 7 Falk, M. and Randell, R.: The lower central series of a fiber-type arrangement, Invent. Math.82 (1985), 77-88. Zbl0574.55010MR808110
  8. 8 Gelfand, I., Goresky, M., MacPherson, R., and Serganova, V.: Geometries, convex polyhedra and Schubert cells, Advances in Math.63 (1987), 301-316. Zbl0622.57014MR877789
  9. 9 Goncharov, G.: Geometry of configurations, polylogarithms and motivic cohomology, Advances in Math.114 (1995), 197-318. Zbl0863.19004MR1348706
  10. 10 Goncharov, A.: Explicit construction of characteristic classes, Advances in Soviet Math.16 (1993), 169-210. Zbl0809.57016MR1237830
  11. 11 Hain, R.: Algebraic cycles and extensions of variations of mixed Hodge structure, Proc. Symp. Pure Math.53 (1993), 175-221. Zbl0795.14005MR1141202
  12. 12 Hain, R.: Classical polylogarithms, in Motives, Proc. Symp. Pure Math., to appear. Zbl0807.19003MR1265550
  13. 13 Hain, R. and MacPherson, R.: Higher Logarithms, Ill. J. Math.34 (1990), 392-475. Zbl0737.14014MR1046570
  14. 14 Hain, R. and Yang, J.: Real Grassmann polylogarithms and Chern classes, Math. Annalen, to appear. Zbl0882.19003
  15. 15 Hain, R. and Zucker, S.: Unipotent variations of mixed Hodge structure, Invent. Math.88 (1987), 83-124. Zbl0622.14007MR877008
  16. 16 Hanamura, M. and MacPherson, R.: Geometric construction of polylogarithms, Duke Math. J.70 (1993), to appear. Zbl0824.14043MR1224097
  17. 17 Hanamura, M. and MacPherson, R.: Geometric construction of polylogarithms, II, preprint, 1993. Zbl0824.14043MR1224097
  18. 18 Kohno, T.: Séries de Poincaré-Kozul associée aux groupes de tresse pure, Invent. Math.82 (1985), 57-75. Zbl0574.55009MR808109
  19. 19 Yang, J.: Algebraic K-groups of number fields and the Hain-MacPherson trilogarithm, Ph.D. Thesis, University of Washington, 1991. 

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