Skip to main content

Differential operators on smooth varieties

  • Conference paper
  • First Online:
Séminaire d’Algèbre Paul Dubreil et Marie-Paul Malliavin

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1404))

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.95
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • A. Beilinson and I.N. Bernstein 1981, Localisation de g-modules, C. R. Acad. Sci. Paris Ser. I 292, pp. 15–18.

    MathSciNet  MATH  Google Scholar 

  • A. Beilinson and I.N. Bernstein 1983, A generalisation of Casselman's submodule theorem in Representation theorey of reductive Lie groups, P.C. Trombi, editor, Progress in Mathematics 40, Birkhäuser Boston 1983.

    Google Scholar 

  • J.N. Bernstein and S.I. Gelfand 1980, Tensor products of finite and infinite dimensional representations of semisimple Lie algebras, Compositio. Math. 41, pp. 245–285.

    MathSciNet  MATH  Google Scholar 

  • A. Borel 1987, Algebraic D-modules, Perspectives in Mathematics 2, Academic Press Boston.

    MATH  Google Scholar 

  • W. Borho 1986, A survey on enveloping algebras of semi-simple Lie algebras I, Canadian Math. Soc. Conf. Proc. 5, pp. 19–50.

    MathSciNet  MATH  Google Scholar 

  • W. Borho and J.-L. Brylinski 1982, Differential operators on homogeneous spaces I, Invent. Math. 69, pp. 437–476.

    Article  MathSciNet  MATH  Google Scholar 

  • W. Borho and J.-L. Brylinski 1985, Differential operators on homogeneous spaces III, Invent. Math. 80, pp. 1–68.

    Article  MathSciNet  MATH  Google Scholar 

  • J.-L. Brylinski 1981, Differential operators on the flag varieties in Tableaux de Young et foncteurs de Schur en algèbre et géométrie, Astérisque 87–88, pp. 43–60.

    MathSciNet  Google Scholar 

  • S.C. Coutinho and M.P. Holland, Module structure of rings of differential operators, Proc. London Math. Soc., to appear.

    Google Scholar 

  • S.C. Coutinho and M.P. Holland 1988, Module structure of the ring of differential operators on projective space, Leeds University preprint.

    Google Scholar 

  • J. Dixmier 1974, Algèbres enveloppantes, Gauthier-Villars Paris.

    Google Scholar 

  • P. Gabriel 1962, Des catégories abéliennes, Bull. Soc. Math. France 90, pp. 323–448.

    MathSciNet  MATH  Google Scholar 

  • R. Hartshorne 1977, Algebraic Geometry, Graduate texts in Mathematics 52, Springer-Verlag Berlin/New York.

    MATH  Google Scholar 

  • T.J. Hodges 1988, K-theory of Noetherian rings, University of Cincinnati preprint.

    Google Scholar 

  • T.J. Hodges and S.P. Smith 1985a, Rings of differential operators and the Beilinson-Bernstein equivalence of categories, Proc. Amer. Math. Soc. 93, pp. 379–386.

    Article  MathSciNet  MATH  Google Scholar 

  • T.J. Hodges and S.P. Smith 1985b, The global dimension of certain primitive factors of the enveloping algebra of a semi-simple Lie algebra, J. London Math. Soc. (2) 82, pp. 411–418.

    Article  MathSciNet  MATH  Google Scholar 

  • T.J. Hodges and S.P. Smith 1985c, Differential operators on projective space, University of Cincinnati preprint.

    Google Scholar 

  • S. Iitaka 1982, Algebraic Geometry, Graduate texts in Mathematics 76, Springer-Verlag Berlin/New York.

    MATH  Google Scholar 

  • A. Joseph 1983, On the classification of primitive ideals in the enveloping algebra of a semi-simple Lie algebra, Lecture notes in Mathematics 1024, Springer-Verlag Berlin/New York.

    MATH  Google Scholar 

  • A. Joseph and J.T. Stafford 1984, Modules of t-finite vectors over semi-simple Lie algebras, Proc. London Math. Soc. (3) 49, pp. 361–384.

    Article  MathSciNet  MATH  Google Scholar 

  • E. Kunz 1985, Introduction to Commutative Algebra and Algebraic Geometry, Birkhäuser Boston.

    MATH  Google Scholar 

  • J.C. McConnell and J.C. Robson 1987, Noncommutative Noetherian rings, John Wiley Chichester/New York.

    MATH  Google Scholar 

  • P. Schapira 1985, Microdifferential Systems in the Complex Domain, Die Grundlehren der Mathematischen Wissenschaften 269, Springer-Verlag Berlin/New York.

    MATH  Google Scholar 

  • J.A. Seebach, L.A. Seebach and L.A. Steen 1970, What is a sheaf?, Amer. Math. Monthly 77ii, pp. 681–703.

    Article  MathSciNet  MATH  Google Scholar 

  • J.-P. Serre 1955, Faisceaux Algébriques Cohérents, Ann. of Math. 61, pp. 197–278.

    Article  MathSciNet  MATH  Google Scholar 

  • J.T. Stafford 1982, Homological properties of the enveloping algebra U(sl2), Math. Proc. Camb. Phil. Soc. 91, pp. 29–37.

    Article  MathSciNet  MATH  Google Scholar 

  • B. Stenström 1975, Rings of Quotients, Die Grundelhren der Mathematischen Wissenschaften 217, Springer-Verlag Berlin/New York.

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Marie-Paule Malliavin

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag

About this paper

Cite this paper

Coutinho, S.C., Holland, M.P. (1989). Differential operators on smooth varieties. In: Malliavin, MP. (eds) Séminaire d’Algèbre Paul Dubreil et Marie-Paul Malliavin. Lecture Notes in Mathematics, vol 1404. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084077

Download citation

  • DOI: https://doi.org/10.1007/BFb0084077

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51812-9

  • Online ISBN: 978-3-540-46814-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics