  We study the multi-wavelength properties of a set of 171 Ly-alpha emitting
candidates at redshift z = 2.25 found in the COSMOS field, with the aim of
understanding the underlying stellar populations in the galaxies. We especially
seek to understand what the dust contents, ages and stellar masses of the
galaxies are, and how they relate to similar properties of Ly-alpha emitters at
other redshifts. The candidates here are shown to have different properties
from those of Ly-alpha emitters found at higher redshift, by fitting the
spectral energy distributions (SEDs) using a Monte-Carlo Markov-Chain technique
and including nebular emission in the spectra. The stellar masses, and possibly
the dust contents, are higher, with stellar masses in the range log M_* = 8.5 -
11.0 M_sun and A_V = 0.0 - 2.5 mag. Young population ages are well constrained,
but the ages of older populations are typically unconstrained. In 15% of the
galaxies only a single, young population of stars is observed. We show that the
Ly-alpha fluxes of the best fit galaxies are correlated with their dust
properties, with higher dust extinction in Ly-alpha faint galaxies. Testing for
whether results derived from a light-weighted stack of objects correlate to
those found when fitting individual objects we see that stellar masses are
robust to stacking, but ages and especially dust extinctions are derived
incorrectly from stacks. We conclude that the stellar properties of Ly-alpha
emitters at z = 2.25 are different from those at higher redshift and that they
are diverse. Ly-alpha selection appears to be tracing systematically different
galaxies at different redshifts.
