Skip to main content
SpringerLink
Log in

Über formale komplexe Räume

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

The formal complex spaces, introduced by Krasnov [24] and independently by the author, are the analytic analogues of the formal schemes of Zariski and Grothendieck. Special cases are the formal completions of complex spaces along analytic sets, see Banica [3]. The technique of formal complex spaces has proved to be a useful tool in analytic geometry and allows even applications to purely algebraic problems, see [24], [4] and [7]. Here the basic theory of these spaces is developed: coherence of the structure sheave, description of the coherent modules, Grauert's coherence theorem for proper maps.... We further study the question of exactness of the formal Dolbeault and de Rham complexes.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literatur

  1. Andreotti,A., Stoll,W.: Analytic and Algebraic Dependence of Meromorphic Functions. Lec. Notes Math.234. Berlin-Heidelberg-New York: Springer 1971

    Google Scholar 

  2. Artin,M.: Algebraization of formal moduli: II.Existence of modifications. Ann. Math.91, 88–135 (1970)

    Google Scholar 

  3. Banica,C.: Le complété formel d'un espace analytique le long d'un sous-espace: Un théorème de comparaison. manuscripta math.6, 207–244 (1972)

    Google Scholar 

  4. Bingener,J.: Divisorenklassengruppen der Komplettierungen analytischer Algebren. Math. Ann.217, 113–120 (1975)

    Google Scholar 

  5. Bingener,J.: Schemata über Steinschen Algebren. Schriftenreihe des Mathematischen Instituts der Universität Münster. 2. Serie, Heft10 (1976)

  6. Bingener,J.: Holomorph-prävollständige Resträume zu analytischen Mengen in Steinschen Räumen. J.f.d.r.u.a.M.285, 149–171 (1976)

    Google Scholar 

  7. Bingener,J.: Über die Divisorenklassengruppen lokaler Ringe. Erscheint demnächst in den Math. Ann.

  8. Bourbaki,N.: Algèbre commutative. Paris: Hermann 1961–1967

    Google Scholar 

  9. Brieskorn,E.: Die Monodromie der isolierten Singularitäten von Hyperflächen. manuscripta math.2, 103–161 (1970)

    Google Scholar 

  10. Cartan,H.: Seminaire 1960/61 2e édition, corrigée (hektographiert)

  11. Godement,R.: Théorie des faisceaux. Paris: Hermann 1964

    Google Scholar 

  12. Grothendieck,A.: Géométrie formelle et géométrie algébrique. Séminaire Bourbaki, t. 11, 1958/59, n° 182

  13. Grothendieck,A.: Cohomologie locale des faisceaux cohérents et Théorèmes de Lefschetz locaux et globaux (SGA 2). Amsterdam: North-Holland Publishing Company 1968

    Google Scholar 

  14. Grothendieck,A., Dieudonné, J.: Eléments de géométrie algébrique. Pub. Math. I.H.E.S.4,8,11,17,20,24,28,32 (1960–1967)

  15. Hakim,M.: Topos annelés et schémas relativs. Berlin-Heidelberg-New York: Springer 1972

    Google Scholar 

  16. Hartshorne,R.: On the de Rham cohomology of algebraic varieties. Pub. Math. I.H.E.S.45 (1975)

  17. Herrera,M., Liebermann,D.: Duality and the De Rham Cohomology of Infinitesimal Neighborhoods. Inventiones math.13, 97–124 (1971)

    Google Scholar 

  18. Hironaka,H.: Resolution of singularities of an algebraic variety over a field of characteristic zero: I,II. Ann. Math.79, 109–326 (1964)

    Google Scholar 

  19. Hironaka,H.: Flattening theorem in complex-analytic geometry. American J. of Math.97, 503–547 (1975)

    Google Scholar 

  20. Hironaka,H.,Matsumura,H.: Formal functions and formal embeddings. J. Math. Soc. Japan20, 52–82 (1968)

    Google Scholar 

  21. Hironaka,H.,Rossi,H.: On the Equivalence of Embeddings of Exceptional Complex Spaces. Math. Ann.156, 313–333 (1964)

    Google Scholar 

  22. Kaup,L.: Eine Künnethforme1 für Fréchetgarben. Math. Z.97, 158–168 (1967)

    Google Scholar 

  23. Kiehl,R., Verdier,J.-L.: Ein einfacher Beweis des Kohärenzsatzes von Grauert. Math. Ann.195, 24–50 (1971)

    Google Scholar 

  24. Krasnov,B.A.: Formal Modifications. Existence Theorems for modifications of complex manifolds. Math. USSR Izvestija Vol.7, 847–881 (1973)

    Google Scholar 

  25. Narasimhan,R.: On the Homology Groups of Stein Spaces. Inventiones math.2, 377–385 (1967)

    Google Scholar 

  26. Reiffen,H.-J.: Das Lemma von Poincaré für holomorphe Differentialformen auf komplexen Räumen. Math. Z.101, 269–284 (1967)

    Google Scholar 

  27. Scheja,G., Storch,U.: Differentielle Eigenschaften der Lokalisierungen analytischer Algebren. Math. Ann.197, 137–170 (1972)

    Google Scholar 

  28. Tougeron,J.-C.: Idéaux de fonctions differentiables. Berlin-Heidelberg-New York: Springer 1972

    Google Scholar 

  29. Wiegmann,K.-W.: Einbettungen komplexer Räume in Zahlenräume. Inventiones math.1, 229–242 (1966)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fachbereich 6 Mathematik/Philosophie, Universität Osnabrück, Albrechtstr. 28, D-4500, Osnabrück

    Jürgen Bingener

Authors
  1. Jürgen Bingener
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bingener, J. Über formale komplexe Räume. Manuscripta Math 24, 253–293 (1978). https://doi.org/10.1007/BF01167833

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01167833

Search

Navigation