The Finiteness Theorem

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

Abstract

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.

Keywords

Hilbert Space Minimal Function Coherent Sheaf Finiteness Theorem Schwarz Lemma 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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