  We present cosmological hydrodynamical simulations of the formation of dwarf
galaxies in a representative sample of haloes extracted from the Millennium-II
Simulation. Our six haloes have a z = 0 mass of ~10^10 solar masses and show
different mass assembly histories which are reflected in different star
formation histories. We find final stellar masses in the range 5 x 10^7 - 10^8
solar masses, consistent with other published simulations of galaxy formation
in similar mass haloes. Our final objects have structures and stellar
populations consistent with dwarf elliptical and dwarf irregular galaxies.
However, in a Lambda CDM universe, 10^10 solar mass haloes must typically
contain galaxies with much lower stellar mass than our simulated objects if
they are to match observed galaxy abundances. The dwarf galaxies formed in our
own and all other current hydrodynamical simulations are more than an order of
magnitude more luminous than expected for haloes of this mass. We discuss the
significance and possible implications of this result.
