Skip to main content

Mixed structures on fundamental groups

  • Chapter
  • First Online:
Realizations of Polylogarithms

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1650))

  • 575 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  • [B] A.A. Beilinson, “Polylogarithm and Cyclotomic Elements”, typewritten preprint, MIT 1989 or 1990.

    Google Scholar 

  • [BBD] A.A. Beilinson, J. Bernstein, P. Deligne, “Faisceaux pervers”, in B. Teissier, J.L. Verdier, “Analyse et Topologie sur les Espaces singuliers” (I), Astérisque 100, Soc. Math. France 1982.

    Google Scholar 

  • [BD] A.A. Beilinson, P. Deligne, “Motivic Polylogarithm and Zagier Conjecture”, preprint, 1992.

    Google Scholar 

  • [BLpp] A.A. Beilinson, A. Levin, “Elliptic Polylogarithm”, handwritten preliminary version of [BLp], June 1991.

    Google Scholar 

  • [BLp] A.A. Beilinson, A. Levin, “Elliptic Polylogarithm”, typewritten preliminary version of [BL], preprint, MIT 1992.

    Google Scholar 

  • [BL] A.A. Beilinson, A. Levin, “The Elliptic Polylogarithm”, in U. Jannsen. S.L. Kleiman, J.-P. Serre, “Motives”, Proc. of Symp. in Pure Math. 55, Part II, AMS 1994, pp. 123–190.

    Google Scholar 

  • [C] K.-T. Chen, “Iterated path integrals”, Bull. AMS 83 (1977), pp. 831–879.

    Article  MathSciNet  MATH  Google Scholar 

  • [CH] J.A. Carlson, R.M. Hain, “Extensions of Variations of Mixed Hodge Structure”, in D. Barlet, H. Esnault, F. El Zein, J.L. Verdier, E. Viehweg, “Actes du Colloque de Théorie de Hodge, Luminy 1987”, Astérisque 179–180, Soc. Math. France 1989, pp. 39–65.

    Google Scholar 

  • [D1] P. Deligne, “Equations Différentielles à Points Singuliers Réguliers”, LNM 163, Springer-Verlag 1970.

    Google Scholar 

  • [D2] P. Deligne, “Théorie de Hodge, II”, Publ. Math. IHES 40 (1971), pp. 5–57.

    Article  MathSciNet  MATH  Google Scholar 

  • [D3] P. Deligne, “La Conjecture de Weil. II”, Publ. Math. IHES 52 (1981), pp. 313–428.

    Google Scholar 

  • [D4] P. Deligne, “Le Groupe Fondamental de la Droite Projective Moins Trois Points”, in Y. Ihara, K. Ribet, J.-P. Serre, “Galois Groups over ℚ”, Math. Sci. Res. Inst. Publ. 16, Springer-Verlag 1989, pp. 79–297.

    Google Scholar 

  • [DG] M. Demazure, P. Gabriel, “Groupes Algébriques”, Tôme 1, North-Holland Publ. Comp. 1970.

    Google Scholar 

  • [DM] P. Deligne, J.S., Milne, “Tannakian Categories”, in P. Deligne, J.S. Milne, A. Ogus K.-y. Shih, “Hodge Cycles, Motives, and Shimura varieties”, LNM 900, Springer-Verlag 1982, pp. 101–228.

    Google Scholar 

  • [FGAIV,3] A. Grothendieck, J. Dieudonné, “Etude locale des Schémas et des Morphismes de Schémas”, Troisième Partie, Publ. Math. IHES 28 (1966).

    Google Scholar 

  • [Ek] T. Ekedahl, “On the Adic Formalism”, in P. Cartier et al. (eds.), “The Grothendieck Festschrift”, Volume II, Birkhäuser 1990, pp. 197–218.

    Google Scholar 

  • [FK] E. Freitag, R. Kiehl, “Etale Cohomology and the Weil Conjecture”, Erg. der Math. und ihrer Grenzgeb., Band 13, Springer-Verlag 1988.

    Google Scholar 

  • [H1] R.M. Hain, “The Geometry of the Mixed Hodge Structure on the Fundamental Group”, in S.J. Bloch, “Algebraic Geometry-Bowdoin 1985”, Proc. of Symp. in Pure Math. 46, Part 2, AMS 1987, pp. 247–282.

    Google Scholar 

  • [H2] R.M. Hain, “Algebraic Cycles and Extensions of Variations of Mixed Hodge Structure”, in J.A. Carlson, C.H. Clemens, D.R. Morrison, “Complex Geometry and Lie Theory”, Proc. of Symp. in Pure Math. 53, AMS 1991, pp. 175–221.

    Google Scholar 

  • [Hi] H. Hironaka, “Resolutions of singularities of an algebraic variety over a field of characteristic zero”, Ann. of Math. 79 (1964), pp. 109–326.

    Article  MathSciNet  MATH  Google Scholar 

  • [Ho] G. Hochschild, “Cohomology of Algebraic Linear Groups”, Illinois Jour. of Math. 5 (1961), pp. 492–519.

    MathSciNet  MATH  Google Scholar 

  • [Hub1] A. Huber, “Calculation of Derived Functors via Ind-Categories”, Jour. of Pure and Appl. Algebra 90 (1993), pp. 39–48.

    Article  MathSciNet  MATH  Google Scholar 

  • [Hub2] A. Huber, “Mixed Perverse Sheaves for Schemes over Number Fields”, to appear in Comp. Math.

    Google Scholar 

  • [Hum1] J.E. Humphreys, “Introduction to Lie Algebras and Representation Theory”, GTM 9, Springer-Verlag 1980.

    Google Scholar 

  • [Hum2] J.E. Humphreys, “Linear Algerbraic Groups”, GTM 21, Springer-Verlag 1987.

    Google Scholar 

  • [HZ1] R.M. Hain, S. Zucker, “A Guide to Unipotent variations of mixed Hodge structure”, in E. Cattani, F. Guillén, A. Kaplan, F. Puerta, “Hodge Theory. Proceedings, Sant Cugat, Spain, 1985”, LNM 1246, Springer-Verlag 1987, pp. 92–106.

    Google Scholar 

  • [HZ2] R.M. Hain, S. Zucker, “Unipotent variations of mixed Hodge structure”, Inv. math. 88 (1987), pp. 83–124.

    Article  MathSciNet  MATH  Google Scholar 

  • [J] U. Jannsen, “Mixed Motives and Algebraic K-Theory”, LNM 1400, Springer-Verlag 1990.

    Google Scholar 

  • [K] A.W. Knapp, “Lie groups, Lie algebras, and Cohomology”, Mathematical Notes 34, Princeton Univ. Press 1988.

    Google Scholar 

  • [Ka] M. Kashiwara, “A Study of Variation of Mixed Hodge Structure”, Publ. RIMS, Kyoto Univ. 22 (1986), pp. 991–1024.

    Article  MathSciNet  MATH  Google Scholar 

  • [P] R. Pink, “Arithmetical compactification of Mixed Shimura Varieties”, thesis, Bonner Mathematische Schriften 1989.

    Google Scholar 

  • [S1] Morihiko Saito, “Modules de Hodge Polarisables”, Publ. RIMS, Kyoto Univ. 24 (1988), pp. 849–995.

    Article  MathSciNet  MATH  Google Scholar 

  • [S2] Morihiko Saito, “Mixed Hodge Modules”, Publ. RIMS, Kyoto Univ. 26 (1990), pp. 221–333.

    Article  MathSciNet  MATH  Google Scholar 

  • [S3] Morihiko Saito, “On the Formalism of Mixed Sheaves”, preprint, RIMS Kyoto (1991).

    Google Scholar 

  • [Sch] W. Schmid, “Variation of Hodge Structure: The Singularities of the Period Mapping”, Inv. math. 22 (1973), pp. 211–319.

    Article  MathSciNet  MATH  Google Scholar 

  • [SGA1] A. Grothendieck et al., “Revêtements Etales et Groupe Fondamental”. LNM 224. Springer-Verlag 1971.

    Google Scholar 

  • [SGA4,II] M. Artin, A. Grothendieck, J.L. Verdier et al., “Théorie des Topos et Cohomologie Etale des Schémas”, Tôme 2, LNM 270, Springer-Verlag 1972.

    Google Scholar 

  • [SGA4,III] M. Artin, A. Grothendieck, J.L. Verdier et al., “Théorie des Topos et Cohomologie Etale des Schémas”, Tôme 3, LNM 305, Springer-Verlag 1973.

    Google Scholar 

  • [SGA4 1/2] P. Deligne et al., “Cohomologie Etale”, LNM 569, Springer-Verlag 1977.

    Google Scholar 

  • [Sp] E.H. Spanier, “Algebraic Topology”, Springer-Verlag 1966.

    Google Scholar 

  • [SZ] J. Steenbrink, S. Zucker, “Variation of mixed Hodge structure, I”, Inv. math. 80 (1985), pp. 489–542.

    Article  MathSciNet  MATH  Google Scholar 

  • [Wo1] Z. Wojtkowiak, “Cosimplicial objects in algebraic geometry”, in “Algebraic K-theory and Algebraic Topology”, Proceedings of the Lake Louise conference 1991 or 1992, Kluwer Academic Publishers 1993, pp. 287–327.

    Google Scholar 

  • [Wo2] Z. Wojtkowiak, “Cosimplicial objects in algebraic geometry II”, preprint. *** DIRECT SUPPORT *** A00I6C03 00002

    Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag

About this chapter

Cite this chapter

Wildeshaus, J. (1997). Mixed structures on fundamental groups. In: Realizations of Polylogarithms. Lecture Notes in Mathematics, vol 1650. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0093053

Download citation

  • DOI: https://doi.org/10.1007/BFb0093053

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62460-8

  • Online ISBN: 978-3-540-49728-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics