  It is now well-known that the surface magnetic fields observed in cool,
lower-mass stars on the main sequence (MS) are generated by dynamos operating
in their convective envelopes. However, higher-mass stars (above 1.5 Msun) pass
their MS lives with a small convective core and a largely radiative envelope.
Remarkably, notwithstanding the absence of energetically-important envelope
convection, we observe very strong (from 300 G to 30 kG) and organised (mainly
dipolar) magnetic fields in a few percent of the A and B-type stars on the MS,
the origin of which is not well understood. In this poster we propose that
these magnetic fields could be of fossil origin, and we present very strong
observational results in favour of this proposal.
