Spaces with finitely generated cohomology

The main result of the paper is the following:Theorem. Suppose all the Cˇech cohomology groups of a space <f>X</f> are finitely generated and <f>Hm(X;Z)</f> is free for some <f>m&ges;2</f>. There is a metrizable space <f>Y∈Cm−1∩LC∞</f> and a map <f>f :X→Y</f> such that <f>f&ast; :Hk(Y;Z)→Hk(X;Z)</f> is an isomorphism for all <f>k&ges;m</f>. If <f>dimX</f> is finite or <f>X</f> is uniformly movable and <f>Hk(X;Z)</f> vanish for large <f>k</f>, then <f>Y</f> is a finite polyhedron. [Copyright &y& Elsevier]