Author: Lionel Schwartz Title: La filtration de Krull de la categorie U et la cohomologie des espaces Jan. 6, 2000 The present paper gives a proof of a conjecture of N. Kuhn : if the mod 2 cohomology of a space has finite Krull filtration in the category of unstable modules, it has to be a locally finite unstable module. Some technical assumptions are required.