manuscripta mathematica

, Volume 58, Issue 4, pp 385–415

Über Differentialoperatoren undD-Moduln in positiver Charakteristik

  • Burkhard Haastert
Article

Abstract

This paper is about differential operators andD-modules on a smooth variety over a field of positive characteristic. Beside some generalities the main results are theD-affinity of the projective space, theD-quasi-affinity of the ordinary flag manifolds (G/B) and theD-affinity of the ordinary flag manifold of Sl3. In contrast to characteristic 0 generally there exists some non-vanishing higher cohomology group of the associated graded algebra gr(D) on an ordinary flag manifold.

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Literatur

  1. [1]
    H. H. ANDERSEN, J. C. JANTZEN: Cohomology of induced representations for algebraic groups. Math. Ann.269, 487–525 (1984)Google Scholar
  2. [2]
    A. BEILINSON, J. BERNSTEIN: Localisation de g-modules. C. R. Acad. Sci.292, 15–18 (1981)Google Scholar
  3. [3]
    I. BERSTEIN: On the dimension of modules and algebras IX, Direct limits. Nagoya Math. J.13, 83–84 (1958)Google Scholar
  4. [4]
    W. BORHO, J. L. BRYLINSKI: Differential operators on homogeneous spaces III, Characteristic varieties of Harish-Chandra modules and primitive ideals. Invent. Math.80, 1–68 (1985)Google Scholar
  5. [5]
    W. BORHO, H. KRAFT: Über Bahnen und deren Deformationen bei linearen Aktionen reduktiver Gruppen. Comment. Math. Helv.54, 61–104 (1979)Google Scholar
  6. [6]
    N. BOURBAKI: Eléments de Mathematique, Algèbre Chap. 1–3, Paris: Herrmann 1970Google Scholar
  7. [7]
    J. L. BRYLINSKI: Differential operators on the flag varieties. In: Young tableaux and Schur functors in algebra and geometry. Asterisque8788, 43–60 (1981)Google Scholar
  8. [8]
    J. L. BRYLINSKI, M. KASHIWARA: Kazhdan-Lusztig conjecture and holonomic systems. Invent. Math.64, 387–410 (1981)Google Scholar
  9. [9]
    S. U. CHASE: On the homological dimension of algebras of differential operators. Commun. Algebra1 (5), 351–363 (1974)Google Scholar
  10. [10]
    E. CLINE, B. PARSHALL, L. SCOTT: A Mackey imprimitivity theory for algebraic groups. Math. Z.182, 447–471 (1983)Google Scholar
  11. [11]
    R. ELKIK: Désingularisation des adhérences d'orbites polarisables et de nappes dans les algèbres de Lie réductives. Preprint, Paris (1978)Google Scholar
  12. [12]
    W. FULTON: Intersection theory. Berlin-Heidelberg-New York: Springer Verlag 1984Google Scholar
  13. [13]
    A. GROTHENDIECK, J. DIEUDONNE: Eléments de Géométrie Algébrique, EGA IV: Etude locale des schemas et de morphismes de schémas. Publ. Math. Inst. Hautes Etud. Sci.20 (1964),24 (1965),28 (1966),32 (1967)Google Scholar
  14. [14]
    B. Haastert: Über Differentialoperatoren undD-Moduln in positiver Charakteristik. Dissertation, Hamburg (1986)Google Scholar
  15. [15]
    W. J. HABOUSH: Central differential operators on split semisimple groups over fields of positive characteristic. In: Séminaire d'Algèbre P. Dubreil et M.-P. Malliavin, Lecture Notes in Math.795, Berlin-Heidelberg-New York: Springer Verlag 1979Google Scholar
  16. [16]
    R. HARTSHORNE: Algebraic geometry. Berlin-Heidelberg-New York: Springer Verlag 1977Google Scholar
  17. [17]
    R. HARTSHORNE: Ample subvarieties of algebraic varieties. Lecture Notes in Math.156, Berlin-Heidelberg-New York, Springer Verlag 1970Google Scholar
  18. [18]
    J. E. HUMPHREYS: Linear algebraic groups. Berlin-Heidelberg-New York: Springer Verlag 1975Google Scholar
  19. [19]
    J. E. HUMPHREYS: Modular representations of classical Lie algebras and semisimple groups. J. Algebra19, 51–79 (1971)Google Scholar
  20. [20]
    J. C. JANTZEN: Über Darstellungen höherer Frobenius-Kerne halbeinfacher algebraischer Gruppen. Math. Z.164, 271–292 (1979)Google Scholar
  21. [21]
    J. C. JANTZEN: Representations of algebraic groups. Erscheint 1987 bei Academic Press.Google Scholar
  22. [22]
    S. P. SMITH: Differential operators on commutative algebras. In: Ring theory. Lecture Notes in Math.1197, Berlin-Heidelberg-New York: Springer Verlag 1986Google Scholar
  23. [23]
    S. P. SMITH: Differential operators on the affine and projective lines in characteristic p>0. Erscheint im Séminaire d'Algèbre P. Dubreil et M.-P. Malliavin.Google Scholar
  24. [24]
    S. P. SMITH: The global homological dimension of the ring of differential operators on a non-singular variety over a field of positive characteristic. Erscheint im J. Algebra.Google Scholar
  25. [25]
    T. A. SPRINGER: Linear algebraic groups. Boston-Basel-Stuttgart: Birkhäuser Verlag 1981Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Burkhard Haastert
    • 1
  1. 1.Mathematisches Seminar der UniversitätHamburg 13Bundesrepublik Deutschland

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