We investigate the evolution of the faint-end slope of the luminosity function , \alpha , using semi-analytical modeling of galaxy formation .
In agreement with observations , we find that the slope can be fitted well by \alpha ( z ) = a + bz , with a = -1.13 and b = -0.1 .
The main driver for the evolution in \alpha is the evolution in the underlying dark matter mass function .
Sub- L _ { * } galaxies reside in dark matter halos that occupy a different part of the mass function .
At high redshifts , this part of the mass function is steeper than at low redshifts , and hence \alpha is steeper .
Supernova feedback in general causes the same relative flattening with respect to the dark matter mass function .
The faint-end slope at low redshifts is dominated by field galaxies and at high redshifts by cluster galaxies .
The evolution of \alpha ( z ) in each of these environments is different , with field galaxies having a slope b = -0.14 and cluster galaxies b = -0.05 .
The transition from cluster-dominated to field-dominated faint-end slope occurs roughly at a redshift z _ { * } \simeq 2 , and suggests that a single linear fit to the overall evolution of \alpha ( z ) might not be appropriate .
Furthermore , this result indicates that tidal disruption of dwarf galaxies in clusters can not play a significant role in explaining the evolution of \alpha ( z ) at z < z _ { * } .
In addition we find that different star-formation efficiencies a _ { * } in the Schmidt-Kennicutt-law and supernovae-feedback efficiencies \epsilon generally do not strongly influence the evolution of \alpha ( z ) .