%0 Journal Article
%T Modular invariants detecting the cohomology of BF_4 at the prime 3
%A Carles Broto
%J Mathematics
%D 2009
%I arXiv
%R 10.2140/gtm.2007.11.1
%X Attributed to J F Adams is the conjecture that, at odd primes, the mod-p cohomology ring of the classifying space of a connected compact Lie group is detected by its elementary abelian p-subgroups. In this note we rely on Toda's calculation of H^*(BF_4;F_3) in order to show that the conjecture holds in case of the exceptional Lie group F_4. To this aim we use invariant theory in order to identify parts of H^*(BF_4;F_3) with invariant subrings in the cohomology of elementary abelian 3-subgroups of F_4. These subgroups themselves are identified via the Steenrod algebra action on H^*(BF_4;F_3).
%U http://arxiv.org/abs/0903.4865v1