Skip to main content

On DG-modules over the de rham complex and the vanishing cycles functor

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1479))

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.95
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Angeniol B.,Lejeune-Jalabert M.Le theoreme de Riemann-Roch singulier pour les D-modules holonomes.-Asterisque,1985,N 130,p.130–160.

    Google Scholar 

  2. Arnold V.I.,Vartchnko A.N.,Gusein-zadet S.M.Singularities of differentiable maps.Part 2.-Moscow,1984 (in Russian).

    Google Scholar 

  3. Deligne P.Les constantes des equations fonctionelles des fonctions L.-IHES preprint,1980.

    Google Scholar 

  4. Bernstein I.N.,Gelfand I.M.,Gelfand S.I.Algebraic vector bundles on pn and problems of linear algebra.-Funkcionalnyi analiz i ego pril.,1978,v.12,N.3,p.66–67 (in Russian).

    MathSciNet  MATH  Google Scholar 

  5. Deligne P.Le formalisme des cycles evanescents.-Lect.Notes in Math.,1973,N.340.

    Google Scholar 

  6. Kashiwara M.Vanishing cycles and holonomic systems.-Lect.Notes inMath.,1983,N.1016,p.134–142.

    Google Scholar 

  7. Kashiwara M.,Shapira P.Microlocal study of sheaves.-Asterisque,1985,N.128.

    Google Scholar 

  8. Laumon G.Sur la categorie derivee filtree des D-modules coherents.-Lect.Notes in Math,1983,N.1016,p.151–237.

    Google Scholar 

  9. Saito M.Modules de Hodge polarisables.-preprimt RIMS,Kyoto univ.,1986,N.553.

    Google Scholar 

  10. Ginsburg V.Characteristic varieties and vanishing cycles.-Invent.Math.,1986,v.84,p.327–402.

    Article  MathSciNet  MATH  Google Scholar 

  11. Priddy S.Koszul complexes.-Trans.Amer.Math.Soc., 1970,v.152,N.1,p.39–60.

    Article  MathSciNet  MATH  Google Scholar 

  12. Beilinson A.A.,Ginsburg V.Mixed categories,Ext-duality and representations.-preprint,Stockholm univ.,1987.

    Google Scholar 

  13. Kapranov M.M.On the derived category and the K-functor of coherent sheaves on intersections of quadrics.-USSR Math Izvestija,1988,v.52,N.1 (in Russian)

    Google Scholar 

  14. Houzel C.,Shapira P.Images directes des modules differentiels.-comptes rendus,1984,t.298,N.18,p.461–464.

    MathSciNet  MATH  Google Scholar 

  15. Eilenberg S.,Moore C.Limits and spectral sequences.-Topology,1962,v.1,N.1,p.1–23.

    Article  MathSciNet  MATH  Google Scholar 

  16. Herrera M.,Lieberman C.Duality and the de Rham cohomology of infinitesimal neighborhoods.-Invent.Math.,1971,v.13,p.97–124.

    Article  MathSciNet  MATH  Google Scholar 

  17. Beilinson A.A.On the derived category of perverse sheaves.-Lect.Notes in Math.,1987,N.1289,p.27–41.

    Google Scholar 

  18. Witten E.Supersymmetry and Morse inequalities.-J.Diff.Geometry,1982,v.17,p.661–692.

    MATH  Google Scholar 

  19. Novikov S.P.Bloch homology.Critical points of functions and 1-forms.-USSR Math.Doklady,1986,v.287,N.6,p.1321–1324 (in Russian).

    MathSciNet  Google Scholar 

  20. Pazhitnov A.V.An analytic proof of the real parts of Novikov's inequalities.-USSR Math.Doklady,1987,v.293,N.6,p.1305, 1307 (in Rissian).

    MathSciNet  MATH  Google Scholar 

  21. Knudsen F.F., Mumford D. The projectivity of the moduli space of stable curves I.-Math.scand.,1976,v.39,N.1,p.19–55.

    MathSciNet  MATH  Google Scholar 

  22. Laurent Y.calcul d'indices et irregularite pour les systemes holonomes.-Asterisque,1985,N.130,p.352–364.

    Google Scholar 

  23. Goresky M.,McPherson R.Stratified Morse theoru.-Springer,1988.

    Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag

About this paper

Cite this paper

Kapranov, M.M. (1991). On DG-modules over the de rham complex and the vanishing cycles functor. In: Algebraic Geometry. Lecture Notes in Mathematics, vol 1479. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086264

Download citation

  • DOI: https://doi.org/10.1007/BFb0086264

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54456-2

  • Online ISBN: 978-3-540-38388-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics