Title: A remark on N. Kuhn's unbounded strong  realization conjecture
Author(s): Gerald Gaudens
Author's e-mail address: gaudens@math.univ-nantes.fr
AMS classification number: 55S10; 57S35

Abstract:

N. Kuhn has given several conjectures on the special features satisfied by the singular cohomology of topological spaces with coefficients in a finite prime field, as modules over the Steenrod algebra. The so-called Realization conjecture was solved in special cases By N. Kuhn and in complete generality by L. Schwartz. The more general Strong realization conjecture has been settled at the prime 2, as a consequence of the work of L. Schwartz, and the subsequent work of F.-X. Dehon and the author. In this note, we are interested in the even more general Unbounded strong  realization conjecture. We shall prove that it holds at the prime $2$ for the class of spaces whose cohomology has a trivial Bockstein action in high degrees.