The Finiteness Theorem

  • Hans Grauert
  • Reinhold Remmert
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 236)


The main purpose of this chapter is to prove the following:

Finiteness Theorem (Cartan, Serre): Let X be a compact complex space. Then for every coherent sheaf S on X all of the cohomology modules H q (X, S), 0 ≤ q ≤ ∞, are finite dimensional ℂ-vector spaces.


Hilbert Space Minimal Function Coherent Sheaf Finiteness Theorem Schwarz Lemma 
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Copyright information

© Springer Science+Business Media New York 1979

Authors and Affiliations

  • Hans Grauert
    • 1
  • Reinhold Remmert
    • 2
  1. 1.Mathematisches InstitutUniversität GöttingenGöttingenFederal Republic of Germany
  2. 2.Mathematisches InstitutWestfälischen Wilhelms-UniversitätMünsterFederal Republic of Germany

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