Progress in our understanding of solar magnetism and activity rest to a large part on our ability to improve spatial resolutionfor resolving the solar surface magnetic fields fine structure. The solarcorona is permeated by magnetic fields emerging from the sun and, inturn, ejects particules and magnetic field into the heliosphere. It isof prime importance to measure the coronal magnetic field to understand mechanisms at work in the corona. We explain why Dome C isexpected to be an outstanding site for such observations and describethe Solar Brightness Monitor we prepare to probe sky background andaerosols levels at this site. We also discuss coronal observations Dome C could allow to obtain.