Résumé :

(with J.A. Crespo and J. Scherer)

In this project we study topological spaces whose loop space has Noetherian mod p cohomology. The aim is to describe the difference between loop spaces with finite mod p cohomology and those whose mod p cohomology is a finitely generated algebra. In the first case, p-complete mod p finite loop spaces lead to the notion of a p-compact group introduced by Dwyer and Wilkerson who showed that then the mod p cohomology of their classifying space is Noetherian. Moreover, p-compacts have been recently classified. We also prove that the classifying space of a loop space with noetherian mod p cohomology has finitely generated mod p cohomology as an algebra over the Steenrod algebra with the following restriction: the module of indecomposable elements belong to the second stage of the Krull filtration U_1 of the category U of unstable modules over the Steenrod algebra.