arXiv version: fonts, pagination and layout may vary from GTM published version Modular invariants detecting the cohomology of BF4 at the prime 3 CARLES BROTO 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 ∗ (BF4; F3) in order to show that the conjecture holds in case of the exceptional Lie group F4. To this aim we use invariant theory in order to identify parts of H ∗ (BF4; F3) with invariant subrings in the cohomology of elementary abelian 3–subgroups of F4. These subgroups themselves are identified via the Steenrod algebra action on H ∗ (BF4; F3). 55R40; 55S10, 13A50 1