Do massive elliptical galaxies contain excess low-mass stars?
In plain words
Spectra and motions of stars in the centers of the biggest galaxies suggest they hold more small, dim stars than the Milky Way does. Some gravitational lensing measurements disagree.
Precise statement
In cores of massive early-type galaxies (velocity dispersion $>2.5x10^7\ \mathrm{cm/s}$), gravity-sensitive absorption features (Na I 8190 Angstrom, Wing-Ford FeH band) and dynamical mass-to-light ratios imply an excess of stars with $m<0.3\ M_{\mathrm{sun}}$ relative to a Milky Way IMF. Determine whether the excess is real, its radial profile, and its dependence on velocity dispersion and metallicity, resolving the disagreement with lensing systems that favor a Milky Way IMF.
What would settle it
Joint stellar-population, dynamical and lensing analysis of the same galaxies with consistent dark matter and stellar population models.